High-Temperature High-Pressure Carbon Dioxide Removal from Coal Gas. Arpaden Silaban Louisiana State University and Agricultural & Mechanical College

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1993 High-Temperature High-Pressure Carbon Dioxide Removal From Coal Gas. Arpaden Silaban Louisiana State University and Agricultural & Mechanical College

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High-temperature high-pressure CO2 removal from coal gas

Silaban, Arpaden, Ph.D.

The Louisiana State University and Agricultural and Mechanical Col., 1993

UMI 300 N.ZeebRd. Ann Arbor, MI 48106

A Dissertation

Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy

The Department of Chemical Engineering

by Arpaden Silaban Engineer, university of Sriwijaya, 1980 M.S. in Ch.E., Louisiana State University, 1989 May 1993

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Debata baen donganmi. Lao mangula ulaonmu. Baen Ibana haposanmu. Sai paserep rohami. Debata baen donganmi. Debata baen donganmi. (..Sian Ende Huria No. 66)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgements

I would like to express my appreciation to Alumni

Professor Douglas P. Harrison as my major advisor. His

initiation, patience, encouragement, and guidance throughout

this study are greatly acknowledged.

Thanks are also due to Professors Frank R. Groves, Jr,

Arthur M. Sterling, and Geoffrey L. Price and Associate

Professor Kerry M. Dooley of the Chemical Engineering

Department, and to Associate Professor Willem H. Koppenol of

the Department of Chemistry for serving as members of

examining committee. Their helpful suggestions and guidance

are appreciated.

I wish to thank Indonesian government via University of

Sriwijaya, Palembang, Indonesia, for financial support during

my study in the United States. In particular, thanks are due

to Professor H. Machmud Hasjim who always supports and

encourages me especially during my final year of study. My

appreciation is also due to Ir. Nawawi Machmud, Ir. H. Ali

Fasya Ismail, M.Eng., and Dr. Ir. Syarifuddin Ismail.

I also would like to thank the Department of Chemical

Engineering for their financial support during my final

semester at LSU.

I am grateful to my friends and fellow graduate students

Muhammad Youvial, Marcel Narcida, and Chun Han who shared

with me during the course of my laboratory work. My

iii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. appreciation also goes to Paul Rodriguez from the machine

shop who always provided me the help during my difficult

times on experimental problems. The help from my student

workers Brandt D. and Matt H. Schumacher are greatly

appreciated.

Finally, my deepest gratitude and love are extended to

my wife, Doorce S. Batubara, and my son, Athens Gomes Partogi

Silaban, who always encourage, motivate, and, most

importantly, pray everyday during our stay at LSU.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS

page

DEDICATION ...... ii

ACKNOWLEDGEMENTS ...... iii

LIST OF TABLES ...... viii

LIST OF FIGURES ...... X

ABSTRACT ...... xviii

Chapter 1: Introduction ...... 1

1.1 Bulk Removal of C02 at High Temperature ...... 5 1.2 Objectives of Current Study ...... 11

Chapter 2: Literature Review ...... 14

2.1 Carbonation of CaO-based Materials . 14 2.2 Structural Property Changes During Calcination of CaC03 ...... 19 2.3 Modeling of Noncatalytic Gas-Solid Reactions ...... 28 2.4 Modeling of Noncatalytic Gas-Solid Reaction with Structural Property Changes ...... 35

Chapter 3: Experimental Apparatus and Procedure 43

3.1 Atmospheric Thermogravimetric Analyzer ...... 43 3.2 High Pressure Electrobalance Reactor S y s t e m ...... 47 3.3 Materials ...... 58 3.4 Experimental Procedure Using High Pressure Electrobalance ...... 60

Chapter 4: Experimental Results: Reaction Screening Tests ...... 66

4.1 Effect of Temperature ...... 67 4.2 Effect of Gas Composition ...... 70 4.3 Comparison of Test Sorbents ...... 79

Chapter 5: Experimental Results: Two-Cycle Reaction Studies ...... 93

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.1 Reactivity and Capacity Indices ..... 98 5.2 Reaction Parameter Evaluation ...... 112 5.3 Direct Comparison of Base Sorbents... 130 5.4 Optimum Reaction Conditions ...... 132

Chapter 6: Experimental Results: Detailed Parametric Studies ...... 134

6.1 Effect of Calcination Pressure ...... 134 6.2 Effect of Calcination Temperature ... 136 6.3 Effect of Carbonation Temperature ... 139 6.4 Effect of Calcination Gas Atmosphere ...... 149 6.5 Conclusions ...... 156

Chapter 7: Experimental Results: Multicycle Studies ...... 160

7.1 Comparison of Sorbent Performance on Five-Cycle Runs ...... 161 7.2 Effect of Calcination Pressure ..... 169 7.3 Effect of Carbonation Temperature ... 174 7.4 Addition of H20 to the Carbonation Gas ...... 174 7.5 C02 Removal from Simulated Coal Gas (H2S-Free) ...... 175 7.6 C02 Removal from Simulated Coal Gas (With H2S) ...... 182 7.7 Ten-Cycle Runs Using Simulated Coal Gas (H2S-Free) ...... 186 7.8 Conclusions ...... 192

Chapter 8: Application of Pore Models with Structural Changes to the Carbonation Reaction ...... 194

8.1 Distributed Pore Size Model ...... 195 8.2 Numerical Solution Technique ...... 203 8.3 Model Parameters ...... 206 8.4 General Discussion of the Solution Characteristics ...... 218 8.5 Comparison between Model Prediction and Experimental Data ...... 225 8.6 Model Predictions with No Pore Diffusion Resistance Using a Modified Pore Size Distribution ...... 241 8.7 Summary ...... 253

Chapter 9: Conclusions and Recommendations for Future Work ...... 256

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. References 265

Nomenclature ...... 272

Appendix A Master List of Runs ...... 275

Appendix B Computer Program of Distributed Pore Size Model ...... 277

Vita 307

vii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES

page

Table 2-1: Structural Properties of Test Sorbents 21

Table 3-1: Cahn 1000 Performance Specifications 49

Table 3-2: Description of Calcium-Based Sorbent Precursos ...... 61

Table 3-3: Chemical Analysis of Reagent Grade CaC03 (as Reported by Mallinckrodt) 62

Table 3-4: Chemical Analysis of Reagent Grade Calcium Acetate (as Reported by Mallinckrodt) ...... 63

Table 3-5: Chemical Analysis of Dolomite (as Reported by National Lime, Co., Findley, Ohio) ...... 63

Table 5-1: Two-Cycle Reaction Parameters ...... 94

Table 5-2: Matrix of Two-Cycle Runs for Sorbent l...... 95

Table 5-3: Matrix of Two-Cycle Runs for Sorbent 7 ...... 96

Table 5-4: Matrix of Two-Cycle Runs for Sorbent 9...... 97

Table 5-5: Summary of the Lag Time, tQ, at Various Reaction Conditions...... 103

Table 5-6: Matrix of First and Second Cycle Reactivity for Sorbent l ...... 105

Table 5-7: Matrix of First and Second Cycle Reactivity for Sorbent 7 ...... 106

Table 5-8: Matrix of First and Second Cycle Reactivity for Sorbent 9 ...... 107

Table 5-9: Matrix of First and Second Cycle Capacity for Sorbent 1 ...... 109

Table 5-10: Matrix of First and Second Cycle Capacity for Sorbent 7 ...... 110

viii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 5-11: Matrix of First and Second Cycle Capacity for Sorbent 9 ...... Ill

Table 5-12: Average and Standard Deviation Values of First and Second Cycle and its Capacity Maintenance for Sorbents 1, 7, and 9 ...... 121

Table 8-1 : Model Prameters Used for Distributed Pore Size Model ...... 207

Table 8-2 : Cumulative Pore Volume as a Function of Pore Diameter for Sorbent 1 (Narcida, 1992) 210

Table 8-3 : Model Parameters Used for General Solution of Ditributed Pore Sie Model ...... 219

Table 8-4 : Model Parameters Whose Values Were Not Changed in Modeling Test HP046 ...... 226

Table 8-5 : Model Parameters Whose Values Were Adjusted in Modeling Test HP046 ...... 226

Table 8-6 : Model Parameters Used for Carbonation Reaction for Run HP066 . . . 235

Table 8-7 : Model Parameters Used for Carbonation Reaction for Run HP049 .... 237

Table 8-8 : Model Parameters Used for Carbonation Reaction for Run HP066 Using Modified Pore Size Distribution ...... 248

Table 8-8 Model Parameters Used for Carbonation Reaction for Run HP049 Using Modified Pore Size Distribution ...... 251

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES

page

Figure 1.1 Equilibrium CO Conversion for the Simultaneous Water-Gas Shift and Carbonation Reactions ...... 9

Figure 1.2 Advanced Gasification/Carbonate Fuel Cell System (from Hauserman et al., 1991) ...... 10

Figure 1.3 Equilibrium C02 Pressure as a Function of Temperature ...... 12

Figure 2.1 CaC03 Calcination and Recarbonation .... 16

Figure 2.2 Pore Size Distribution of As-Received Calcium Carbonate and after Calcination at 750 C in N2 Atmosphere for 1 hour (Narcida, 1992) ... 22

Figure 2.3 Pore Size Distribution of As-Received Calcium Acetate and after Calcination Temperatures in N2 Atmosphere...... 24

Figure 2.4 Pore Size Distribution of As-Received Dolomite and after Calcination at 750 C in N2 Atmosphere for 1 h o u r ...... 25

Figure 2.5 Variation of Sulfation Rate with the Porosity of the Natural Rock (from Hartman et al., 1978) ...... 27

Figure 2.6 Schematic of the Unreacted Core Model .. 30

Figure 2.7 Schematic of the Volumetric Model ...... 32

Figure 2.8 Schematic of the Grain M o d e l ...... 33

Figure 2.9a Schematic Representation of the Pore Model (from Szekely and Evans, 1970) ... 34

Figure 2.9b The Reaction Front in the Pore Model (from Szekely and Evans, 1970) ...... 34

Figure 2.10 Modified Grain Model (from Ranade and Harrison, 1979) ...... 37

Figure 2.11 Geometric Changes in a Single Pore M o d e l ...... 39 x

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.1 Schematic Diagram of Atmospheric TGA ... 44

Figure 3.2 Typical Response of Atmospheric Pressure TGA ...... 46

Figure 3.3 Schematic Diagram of High Pressure TGA ...... 48

Figure 3.4 Typical High Pressure Response ...... 52

Figure 3.5 Typical Response Using Water Vapor .... 55

Figure 3.6 Diagram of Insert Added to the Hangdown Tube ...... 57

Figure 3.7 TGA Response Using Water Vapor ...... 59

Figure 4.1 Effect of Temperature on Calcination Kinetics; Sorbent 1 ...... 68

Figure 4.2 Effect of Temperature on Carbonation Kinetics; Sorbent 1 ...... 69

Figure 4.3 Long-Term Carbonation Results; Sorbent 1 ...... 71

Figure 4.4 Effect of C02 Concentration on Carbonation Kinetics; Sorbent 1 ...... 72

Figure 4.5 Effect of Gas Composition on Carbonation Kinetics; Addition of CO and H2; Sorbent 1 ...... 73

Figure 4.6 Testing for the Presence of the Shift Reaction; Sorbent 1 ...... 75

Figure 4.7 Carbonation Kinetics with Constant C02 Concentration and Varying Background Gas Composition; Sorbent 1 ...... 76

Figure 4.8 Carbonation with no C02 in the Feed Gas; Sorbent 1 ...... 78

Figure 4.9 Comparison of Calcination Kinetics; Sorbents 1, 2, 4, and 5 ...... 80

Figure 4.10 Comparison of Calcination Kinetics; Sorbents 1, 3, and 6 ...... 81

Figure 4.11 Comparison of Carbonation Kinetics; Sorbents 1, 2, 4, and 5 ...... 83

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.12 Comparison of Carbonation Kinetics; Sorbents 1, 3, and 6 ...... 84

Figure 4.13 Decomposition and Carbonation Kinetics; Sorbent 7 ...... 86

Figure 4.14 Decomposition of Calcium Sulfate; Sorbent 8 ...... 88

Figure 4.15 Calcination and Carbonation Kinetics; Sorbent 9 ...... 90

Figure 4.16 Comparison of First-Cycle Carbonation Kinetics; Sorbents 1, 7, and 9 ...... 92

Figure 5.1 Reaction Reproducibility of Two Calcination-Carbonation Cycles for Sorbent 9 ...... 99

Figure 5.2 Determination of the Time Lag, tc, during Carbonation Reaction ...... 101

Figure 5.3 Effect of Calcination Temperature on First-Cycle Reactivity and Capacity .... 113

Figure 5.4 Effect of Calcination Temperature on Second-Cycle Reactivity and Capacity ... 114

Figure 5.5 Effect of Calcination Temperature on Reactivity Maintenance...... 115

Figure 5.6 Effect of Calcination Temperature on Capacity Maintenance...... 116

Figure 5.7 Effect of Carbonation Temperature on First-Cycle Reactivity; Carbonation at 1 atm in 15% C02-N2 ...... 119

Figure 5.8 Effect of Carbonation Temperature on First-Cycle Reactivity; Carbonation at 15 atm in 15% C02-N2 ...... 120

Figure 5.9 Effect of Carbonation Temperature on Average Capacity Maintenance ...... 123

Figure 5.10 Effect of Carbonation Pressure on First-Cycle Reactivity ...... 125

Figure 5.11 Effect of Carbonation Pressure on Capacity Maintenance...... 127

xii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5.12 Effect of C02 Mol Fraction on First- Cycle Reactivity...... 128

Figure 5.13 Effect of C02 Mol Fraction on First- Cycle Capacity ...... 129

Figure 6.1 Comparison of Calcination Kinetics at Different Pressure; Sorbent 9 ...... 135

Figure 6.2 Effect of Calcination Pressure on First-Cycle Carbonation Kinetics; Sorbent 7 ...... 137

Figure 6.3 Calcination Kinetics as a Function of Temperature; Sorbent 7 ...... 138

Figure 6.4 Effect of Calcination Temperature on First-Cycle Carbonation Kinetics; Sorbent 7 ...... 140

Figure 6.5 Effect of Calcination Temperature on Capacity Maintenance; Sorbent 7 ...... 141

Figure 6.6 Effect of Temperature on Carbonation Kinetics During Early Phases of the Reaction; Sorbent 9 ...... 142

Figure 6.7 Effect of Carbonation Temperature on Capacity Maintenance; Sorbent 9 ...... 144

Figure 6.8 Effect of Temperature on Carbonation Kinetics; Sorbent 7 ...... 145

Figure 6.9 Effect of Carbonation Temperature on Capacity Maintenance; Sorbent 7 ...... 147

Figure 6.10 Effect of Carbonation Temperature on Capacity Maintenance; Sorbent 7 ...... 148

Figure 6.11 Effect of Gas Atmosphere on Calcination Kinetics; Calcination at 900°C, Sorbent 1 150

Figure 6.12 Effect of Calcination Gas Atmosphere on First-Cycle Carbonation Kinetics; Calcination at 900°C, Sorbent 1 ...... 151

Figure 6.13 Effect of Gas Atmosphere on Calcination Kinetics; Calcination at 825°C, Sorbent 1 ...... 154

xiii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 6.14 Effect of Calcination Gas Atmosphere on First-Cycle Carbonation Kinetics; Calcination at 825°C, Sorbent 1 ...... 155

Figure 6.15 Effect of Gas Atmosphere on Calcination Kinetics; Calcination at 750°C, Sorbent 1 ...... 157

Figure 6.16 Effect of Calcination Gas Atmosphere on First-Cycle Carbonation Kinetics; Calcination at 750°C, Sorbent 1 ...... 158

Figure 7.1 Calcination-Carbonation Results for Sorbent 1 Through Five Cycles ...... 162

Figure 7.2 Comparison of Capacity Decrease for Sorbent 1 with Literature Results at Similar Reaction Conditions ...... 164

Figure 7.3 Carbonation Results for Sorbent 7 Through Five C y c l e s ...... 165

Figure 7.4 Carbonation Results for Sorbent 9 Through Five C y c l e s ...... 166

Figure 7.5 C02 Capacity per Gram of Sorbent for Four Sorbents as a Function of Cycle N u m b e r ...... 168

Figure 7.6 Five-Cycle Reactivity and Capacity of Sorbent 7 as a Function of Calcination Pressure; Carbonation at 650°C ...... 170

Figure 7.7 Five-Cycle Reactivity and Capacity of Sorbent 9 as a Function of Calcination Pressure; Carbonation at 650°C ...... 171

Figure 7.8 Five-Cycle Reactivity and Capacity of Sorbent 7 as a Function of Calcination Pressure; Carbonation at 750°C ...... 172

Figure 7.9 Five-Cycle Reactivity and Capacity of Sorbent 9 as a Function of Calcination Pressure; Carbonation at 750°C ...... 173

Figure 7.10 First-Cycle Carbonation Kinetics of Sorbent 9 in Different Gas Atmospheres...... 176

Figure 7.11 Five-Cycle Capacity of Sorbent 9 as a Function of Carbonation Gas Atmosphere...... 177 xiv

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 7.12 Five-Cycle Capacity of Sorbent 7 as a Function of Carbonation Gas Atmosphere...... 178

Figure 7.13 First-Cycle Carbonation Kinetics of Sorbent 9 using Three Different Gas Atmospheres...... 181

Figure 7.14 Weight-Time Response during Multicycle Carbonation of Sorbent 9 with H2S in the Reacting G a s ...... 183

Figure 7.15 Build-Up of Calcium Sulfide during Carbonation Cycles ...... 185

Figure 7.16 Carbonation Kinetics of Sorbent 7 in the First, Fifth, and Tenth Cycles .... 187

Figure 7.17 Carbonation Capacity Versus Cycle Number for Ten-Cycle Runs Using Sorbent 7 ...... 188

Figure 7.18 Carbonation Kinetics of Sorbent 9 in the First, Fifth, and Tenth Cycles .... 190

Figure 7.19 Carbonation Capacity Versus Cycle Number for Ten-Cycle Runs Using Sorbent 9 ...... 191

Figure 8.1 Geometric Changes During Reaction in a Single Pore (Christman and Edgar, 1983) ...... 197

Figure 8.2 Flowchart for the Distribution Pore Size M o d e l ...... 204

Figure 8.3 Cumulative Pore Volume as a Function of Pore Diameter Used for General Discussion of the Solution Characteristics ...... 220

Figure 8.4 Model Prediction of Conversion-Time Results Using Parameters in Table 8-3 and Initial Pore Size Distribution in Figure 8 . 3 ...... 221

Figure 8.5 Local Porosity as a Function of Radial Position within the Particle with the Reaction Time as a Parameter; Significant Pore Diffusion Resistance within the Particle...... 223

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 8.6 Effect of Initial Particle Porosity on Maximum Achievable Conversion with Negligible Pore Diffusion Resistance; Of 2.20 ...... 224

Figure 8.7 Comparison between Model Predictions and Experimental Data of Run HP046 ..... 227

Figure 8.8 Comparison between Model Prediction and Experimental Data of Run HP043; Effect of C02 Mol Fraction ...... 230

Figure 8.9 Comparison between Model Prediction and Experimental Data of Run HP137; Effect of C02 Carbonation Pressure ..... 232

Figure 8.10 Comparison between Model Predictions and Experimental Data of Run HP066; Carbonation at 750°C and 1 atm in 15% C02/N2 ...... 234

Figure 8.11 Comparison between Model Predictions and Experimental Data of Run HP049; Carbonation at 550°C and 1 atm in 15% C02/N2 ...... 238

Figure 8.12 Comparison between Predicted Maximum Conversions and Experimental "Maximum" Conversion at Different Carbonation Temperatures ...... 240

Figure 8.13 Comparison between Model Prediction and Experimental Data of Run HP046 Using Modified Pore Size Distribution ... 243

Figure 8.14 Comparison between Model Prediction and Experimental Data of Run HP043 Using Modified Pore Size Distribution ... 245

Figure 8.15 Comparison between Model Prediction and Experimental Data of Run HP137; Effect of Carbonation Pressure, Using Modified Pore Size Distribution...... 246

Figure 8.16 Comparison between Model Predictions and Experimental Data for Run HP066; Carbonation at 750°C and 1 atm in 15% C02/N2, Using Modified Pore Size Distribution...... 249

xvi

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure .17 Comparison between Model Predictions and Experimental Data for Run HP049; Carbonation at 550°C and 1 atm in 15% C02/N2, Using Modified Pore Size Distribution ...... 252

xvii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract

The noncatalytic gas-solid reaction between C02(g) and

CaO(s) to form CaC03(s) has been studied at high temperature

and high pressure (HTHP) using a thermobalance reactor. This

reaction could serve as the basis for a HTHP process for the

separation of C02 from coal-derived gas.

The kinetics of the calcination and carbonation

reactions were studied as a function of temperature,

pressure, C02 concentration, and background gas composition.

Three sorbent precursors which produced CaO having a wide

range of structural properties were selected for detailed

kinetic studies. They were (i) reagent grade calcium

carbonate, (ii) reagent grade calcium acetate, and (iii)

commercial grade dolomite containing essentially equimolar

quantities of CaC03 and MgC03. Multicyle runs were conducted

in order to have a better understanding of sorbent

durability. Almost complete carbonation was possible using

both calcium acetate and dolomite sorbent precursors;

carbonation was incomplete when calcium carbonate precursor

was used.

The following operating conditions were found to be most

appropriate:

Calcination temperature: 750°C

Calcination pressure : 1 - 15 atm

xviii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Calcination atmosphere : any inert gas with low

C02 partial pressure

Carbonation temperature : 650 - 750°C

Carbonation pressure : 15 atm

Carbonation atmosphere : any sulfur-free or low-

sulfur coal gas

When sulfur-free simulated coal gas was tested, improved

sorbent reactivity, capacity, and capacity maintenance were

observed. The increase in reactivity was consistent with a

higher concentration of C02, possibly formed by the water-gas

shift reaction.

The distributed pore size model (Christman and Edgar,

1983) was used to analyze the carbonation results using the

reagent grade calcium carbonate precursor. Good agreement

between the model and experiment was achieved for runs at

650°C with varying C02 mol fraction and reaction pressure. At

different carbonation temperatures, however, it was necessary

to assign zero activation energies to the intrinsic rate

constant and product layer diffusion coefficient in order to

match the experimental data. Both of these parameters should

have quite large activation energies.

xix

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 1

Introduction

Improved coal gasification technology is important if

the vast reserves of coal available world-wide are to be used

in a manner which is economically attractive and

environmentally acceptable. A number of studies have focused

on the improvement of energy efficiency in coal gasification

for electric power generation. Integrated gasification

combined-cycle (IGCC) power plants are reported to have an

energy efficiency as high as 42.7% while the integration of

currently available gasification processes with molten

carbonate fuel cells (MCFCs) is expected to have 52.5% energy

efficiency (Holt, 1991). These efficiency values may be

compared to typical 37% efficiencies achieved in current

pulverized coal fired power plants.

While the improved energy efficiency of coal

gasification can be achieved, reducing or removing the

adverse environmental impact associated with coal utilization

has also been a major concern. Removal of trace gas

impurities such as H2S, COS, and N0X is necessary before

coal-gases are used in further processes. Conventional

removal of these trace contaminants is accomplished by wet

scrubbing operations which require that the hot coal-gas be

cooled to near ambient temperature before treatment.

The low-temperature wet removal causes a loss in thermal

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. efficiency and additional capital equipment cost for

necessary heat exchangers is inevitably required. Further

improvements in overall efficiency would be possible if

contaminant removal could be accomplished at elevated

temperature.

Contaminants in the coal gas, such as sulfur and

nitrogen species, particulate matter, and trace metals and

alkali, are detrimental to the operation of both turbines and

fuel cells. These contaminants must be removed in order to

reduce the capital cost and, at the same time, increase the

overall cycle efficiency for the power plant. Removal of H2S

to less than 10 ppmv can minimize the corrosion of turbine

blades. Removal of H2S to less than 1 ppmv may be necessary

to avoid the poisoning of electrodes in molten carbonate fuel

cells (Gangwal et a l ., 1989).

For a number of years research at LSU has focused on

high-temperature coal-gas desulfurization based upon the

noncatalytic gas-solid reaction between H2S and appropriate

metal oxides. Westmoreland and Harrison (1976) performed a

preliminary thermodynamic analysis of various metal oxides as

candidate sorbents for gas desulfurization. Using the free

energy minimization method, they reported that eleven

candidate solids based upon the metals Fe, Zn, Mo, Mn, V, Ca,

Sr, Ba, Co, Cu, and W were thermodynamically feasible for

high temperature desulfurization of low-Btu gas. Westmoreland

et a l . (1977) then performed comparative kinetic studies of

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the high temperature reaction between H2S and selected metal

oxides (MnO, ZnO, CaO, and V203) over the temperature range of

300-800°C in a thermogravimetric analyzer. Gibson and

Harrison (1980) studied the kinetics of the reaction between

H2S and ZnO pellets in a microbalance over the temperature

range of 375-800°C. Rapid and essentially complete reaction

was observed in the temperature range of 600-700°C while slow

decomposition of ZnO with subsequent zinc vaporization was

observed near 800°C. At temperatures below 600°C, the

reaction stopped well before total ZnO conversion was

obtained. Ranade and Harrison (1981) examined the effect of

structural property changes during the ZnO-H2S reaction.

Focht et al. (1988) studied the kinetics of the reaction

between zinc ferrite, ZnFe204, and H2S in the temperature

range of 500-700°C. Reduced zinc ferrite in the form of ZnO

plus Fe304 was found to be capable of rapid and complete

reaction with H2S at the temperatures of interest. More

interestingly, Focht et al. (1989) reported that zinc ferrite

sorbents were capable of being regenerated and subjected to

a number of cycles without suffering a major activity loss.

Woods et al. (1990) investigated the single pellet reaction

between H2S and zinc oxide-titanium oxide sorbents in an

electrobalance reactor at the temperature range of 670-760°C.

The addition of titanium oxide was believed to reduce the

tendency for zinc oxide reduction and subsequent

volatilization of metallic zinc, thereby increasing the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. maximum sorbent operating temperature. Woods et al. (1991)

also studied the reaction kinetics of another zinc ferrite

sorbent having different structural properties using a

thermogravimetric reactor as a function of temperature,

pressure, gas composition, and sorbent radius over the

temperature range of 500-700°C. H2S concentration, reaction

pressure, and sorbent radius had a strong effect on

sulfidation kinetics. The sulfidation kinetics, however, were

essentially independent of temperature in the 500-700°C

range. More recently, Silaban et al. (1991) investigated zinc

ferrite sorbents prepared using a number of formulation

recipes and induration conditions with the objective of

determining which sorbent formulations had a high reactivity

and, most importantly, durability.

Similar research has been carried out by a number of

researchers at other locations. Lew (1990) and Lew et a l .

(1992a), for example, studied the potential benefit of

reduction and sulfidation of zinc titanate compared to zinc

oxide solids. It was found that zinc titanate was reduced

more slowly to volatile elemental zinc than pure zinc oxide.

H2S removal using metal oxides at high temperature has

also been tested in larger scale reactors. Grindley and

Steinfeld (1981) studied the desulfurization of simulated

coal gas using zinc ferrite sorbents in a fixed-bed reactor.

They reported that zinc ferrite sorbents were capable of

reducing H2S to 5 ppm. Sorbents other than zinc ferrite (zinc

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. titanate, zinc copper ferrite, copper aluminate, etc.) have

been tested in a fixed-bed at the bench-scale level using a

simulated coal gas (Gangwal et al., 1988). Zinc titanate was

shown to be a promising sorbent at up to 150°F higher

operating temperature than zinc ferrite. Pilot scale tests of

a hot gas cleanup system using zinc ferrite were also

performed by KRW Energy System, Inc. (Schmidt et al., 1988),

the M.W. Kellog Company (Buckman et al., 1988), GE

Environmental Services (Cook et al., 1988), and Texaco Inc.

(Robin et al., 1988).

While the removal of trace components from coal gases

at high temperature has been studied extensively and has

proven to be feasible, it is also desirable to separate bulk

gasifier products in order to achieve further improvements in

gasification process efficiency and economics. The U.S.

Department of Energy has identified the need for bulk

separation processes which would operate within a temperature

range of 100-700°C. Typical bulk gas components produced from

coal gasification are carbon dioxide, carbon monoxide,

hydrogen, nitrogen, and methane.

l.l Bulk Removal of C02 at High Temperature

Bulk removal of C02 can improve the performance of

several downstream processes which utilize the coal gas.

Examples are increased heating value of the fuel gas,

increased efficiency of the shift conversion process for

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. production of hydrogen or methanol and ammonia synthesis gas,

and the improved operation of molten carbonate fuel cells.

The production of hydrogen will be described as an example.

Coupling the well-known shift reaction for hydrogen

production with C02 removal at high temperature could improve

the efficiency of the process. Consider the water-gas shift

reaction:

CO + H20 * C02 + H2 (1 -1)

Multiple catalytic reactors are normally required

because the exothermic reaction is highly reversible. The

"high" temperature shift catalyst , which normally operates

in the 350-450°C range, consists of chromia-promoted iron

oxide. The "low" temperature catalyst, operating at the

temperature range of 200-250°C, consists of copper and zinc

oxides supported on A1203. A serious problem associated with

low temperature catalysts is the possibility of catalyst

poisoning by sulfur compounds. This problem could be more

serious when the synthesis gas is derived from coal

gasification because of the sulfur content.

Removing the C02 as it is formed will avoid the

equilibrium limitation and increase the yield of H2. This can

be done by direct coupling between reaction (1.1) and

reaction (1.2):

+ C02(g) ** CaC03(s) (1*2)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The concept of simultaneous high-temperature C02 removal and

shift reaction was first proposed by Gluud et al. (1931) and

later revived by Squires (1967) . However, the concept was not

economically competitive at that time due to the availability

of reliable and low-cost methods of C02 removal near ambient

temperature.

A brief thermodynamic analysis will illustrate the

potential of combining the high temperature shift reaction

with C02 removal. The equilibrium constant for the shift

reaction (1.1) is

KPi = E s k h k (i-i) P ccP h2o

Kpt as a function of temperature may be calculated using the

thermochemical constants of Barin and Knacke (1973):

log !„*£>!= a + bT + c T 2 + dT2 + er4 (1-2)

where a = 10.56, b = -2.9E-02, c = 3.06E-05, d = -1.41E-08,

and e = 2.07E-12. The equilibrium constant for reaction (1.2)

Kpz = -±- (1-3) Pco2

Kp2 can be expressed as a function of temperature (Barin and

Knacke, 1973):

log10i

where a = 47.69, b = -0.13, c = 0.14E-03, d = -0.75E-07, and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. e = 0.15E-10. An expression for the overall equilibrium for

the combined reactions is

Ka = KP l KPz = - A ■ (1-5) c C0 c H20

Figure 1.1 illustrates the equilibrium calculation for a

typical synthesis gas composition consisting of 18.9%(mol)

H2, 3.0% CO, 2.5% C02/ and 75.6% H20. At 723 K, for example,

the equilibrium fractional conversion of CO without using CaO

for C02 removal (curve A) is only 93%. Using the combined

reactions at 1 atm (curve B), the equilibrium CO conversion

is essentially complete for all temperatures less than about

800 K. Moreover, at 22.1 atm (curve C) essentially complete

CO conversion is feasible to about 900 K. When the CaC03

decomposition temperature is approached, the equilibrium C02

pressure increases and equilibrium CO conversion approaches

the level corresponding to the shift reaction alone.

As a second example, separation of C02 from coal-derived

gas before being fed to a molten carbonate fuel cell can

improve the overall system efficiency. Figure 1.2 (from

Hauserman et al., 1991) shows a diagram of a conceptual

advanced gasification and molten carbonate fuel cell system.

"Clean" coal-derived gas is sent to a C02 separation section

leaving H2 and CO which are sent to the anode part of a

molten carbonate fuel cell while the separated C02 is

directed to the cathode. This approach can improve the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9

CO + H20 <==> C02 + H2

Inlet Gas Composition (mol X): H218.9 H20 75.6

CO 3.0 C02 1 5 1 1 1 1 1 1 1 1 1 1 1 1--- 500 600 700 800 900 1000 1100 TEMPERATURE, K

Figure 1.1 Equilibrium CO Conversion for the Simultaneous Water-Gas Shift and Carbonation Reactions

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o

I Steam Cycle HRSG Bottoming A.C. Power

Heat

D.C. Power Fuel Cell Carbonate CO H 2 , CO c o 2 Separation (from Hauserman etal., 1991) Fuel Cell Exhaust CO H 2 , CO Figure 1.2 Advanced Gasification / Carbonate Fuel Cell System Gasifier Coal Steam

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11

overall efficiency from about 46% without C02 separation to

about 53% with C02 separation (Hauserman et al., 1991).

1.2 Objectives of Current Study

High temperature C02 removal from simulated coal-gas has

been studied by utilizing the reversible noncatalytic gas-

solid reaction with calcium oxide, reaction (1-2). Figure 1.3

shows calculated values of the equilibrium ptressure of C02

over CaO for the temperature range of 773 to 1273 K using

Gibbs free energy data from Hougen et a l . (1959). In many

gasification processes the product gas is at a temperature of

500 to 700°C and a pressure of 5 atm or higher. With a

relatively high C02 content in the gasifier product (e.g., 15

volume%) C02 removal (forward reaction) is favored at the

above temperatures and pressures. Moreover, the reverse

reaction may be accomplished by lowering the operating

pressure, reducing C02 partial pressure, and/or increasing

the operating temperature. For coal gas entering at 650°C, 15

atm and containing 15% C02, for example, it is theoretically

possible to achieve 99.6% C02 removal. With lower

temperatures, higher pressures, and/or higher inlet C02

concentrations, greater C02 removal efficiencies are

theoretically possible.

The objective of this research has been to determine the

technical feasibility of C02 separation using a CaO-based

sorbent at high temperature and high pressure by performing

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12

Ca0(s)+C02(g) <— > CaC03(s) 1E+01- P(C02)= 1/K

cs IE -0 1 - 8

1 E -0 2 -

1 E -0 3 -

1E-04 800 900 1000 1100 1200 1300 1400 1500 TEMPERATURE, K

Figure 1.3. Equilibrium C02 Pressure as a Function of Temperature

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kinetic studies to determine the effect of operating

conditions, sorbent properties, and multicycle operation in

laboratory scale equipment.

Structural properties of "fresh" sorbents and after

being subjected to various reaction conditions, from the

related study of Narcida (1992), are used to support the

kinetic studies.

In addition, the experimental results have been analyzed

using an appropriate gas-solid reaction model in order to

better understand the behavior of the reaction.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 2

Literature Review

The literature review focuses on three major areas. The

first concerns previous studies on carbonation of CaO-based

materials. The second major area concerns the structural

property changes which occur during calcination of CaC03 and

subsequent carbonation of CaO. The discussion includes the

similar behavior associated with the CaO + S02 reaction.

Numerous studies of this reaction have been performed due to

the need for removing sulfur compounds in flue gas

desulfurization. Finally, mathematical models for describing

the reaction between a gas and a porous solid whose

structural properties change will be reviewed.

2.1 Carbonation of CaO-based Materials

The possibility of using the carbonation reaction for

C02 removal was considered at least as early as the 1920s.

Gluud et al. (1931) patented a process for producing hydrogen

via the water-shift reaction using calcined dolomite as a

combination shift catalyst-C02 sorbent in a fixed bed

reactor. They found that MgO served as a catalyst in CO

conversion while CaO reacted with C02 to form CaC03. Squires

(1967) revived the concept and suggested the use of dual

fluidized-bed reactors to permit steady-state operation and

overcome other problems associated with Gluud's concept. The

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15

C02 acceptor process (Curran et al., 1967) was based upon the

simultaneous removal of H2S and C02 from coal-derived gases.

Dolomite was again used as the solid sorbent. Since each of

these studies was process oriented, essentially no

fundamental kinetics data were reported.

Dedman and Owen (1962) performed a more fundamental

study of the carbonation of CaO. They studied the reaction at

the temperature range of 100-600°C using various C02

pressures. The reaction of C02 with calcined limestone

occured in two stages; a very rapid initial reaction was

followed by an abrupt transition to a much slower reaction

well before all calcium was reacted. The rapid stage was

reported to be due to chemisorption and reaction of C02 on

the surface while the slower reaction stage was due to the

diffusion of the gases in pores at the lower temperature and

migration of the ions at higher temperature (above 300°C).

Barker (1973) examined the reaction between C02 and CaO

at 866°C in a thermogravimetric analyzer using calcium

carbonate of particle diameter of 2 to 20 microns. Figure 2.1

shows the typical response found when CaC03 was subjected to

multiple calcination and carbonation cycles. As seen in the

figure, calcination was always complete (56 weight %). The

carbonation reaction, however, was initially rapid and after

reacting to approximately 72% carbonation, the reaction rate

quickly dropped off well short of completion. 98% carbonation

was achieved after 24 hours. Barker also found that

Weigh! of somple (% ) 100 90 80 70 60 50 (b ) Multiple Short Cycles Short (b) Multiple (a) Recarbonation hr. 24 fo akr 1973)(fromBarker/ ie (h) Time

16 17

carbonation gradually decreased with multiple cycles as a

result of the loss of pore volume in the CaO and possibly

sintering of the carbonate. In a subsequent study, Barker

(1974) utilized very small particles (diameter of about 20

nm) in order to achieve complete carbonation with no

deterioration as the number of cycles increased. While

complete reaction was achieved, the use of such a particle

size is commercially difficult.

Delucia (1985) studied multicycle carbonation runs in a

TGA at atmospheric pressure over the temperature range of 50

to 800°C. Calcined samples were reported to have a smaller

particle volume than the starting calcium carbonate

materials. The particles shrank from 7.4 to 24%, depending on

calcination conditions. The reactivity of the particles also

declined 10 to 25% per cycle. The multicycle decline was

similar to that reported by Barker (197 3).

Bhatia and Perlmutter (1983) studied the carbonation

reaction over the temperature range of 400 to 725°C in a

thermogravimetric analyzer at atmospheric pressure. They

reported similar behavior, an initially rapid reaction

controlled by the surface resistance followed by a much

slower reaction controlled by product layer diffusion.

The incomplete reaction during the carbonation phase can

be explained by considering structural property changes in

the course of reaction. Precursor calcium carbonate or

limestones are effectively nonporous. During calcination,

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product gas C02 must escape from the solid structure thereby

creating pores within the solid CaO. In principle, the pore

volume created during calcination should be sufficient so

that complete recarbonation of the CaO could occur. In

practice, however, recarbonation occurs preferentially near

the particle exterior and the surface porosity approaches

zero preventing C02 from reaching unreacted CaO at the

interior of the particle. During the slow reaction phase

either C02 must diffuse through a nonporous carbonate layer

or unreacted CaO must diffuse outward to complete the

reaction with C02.

By preventing pore closure during the carbonation

reaction, it is expected that the extent of reaction would

increase. Dhupe et al. (1987) and Dhupe and Gokarn (1990)

added metallurgica1-grade silicon powder to CaO as an inert

material. After 3 hours, 78% carbonation was achieved for

calcined CaC03 with 70% inert material compared to only about

45% conversion for pure CaO. An optimum inert composition was

proposed in order to achieve the maximum capacity, but with

no clear explanation.

Beruto et al. (1988) studied the use of calcium

precursor materials other than CaC03 which, upon calcination,

would increase the initial porosity of CaO and allow complete

carbonation. Calcium acetate and calcium oxalate were used as

the CaO precursors. With calcium acetate precursor, 90%

carbonation was achieved in less than 1% hours, compared to

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19

60% carbonation using calcium carbonate precursor at the same

reaction conditions.

Oakeson and Cutler (1979) studied the diffusion-

controlled reaction using nonporous CaO in a microbalance

over the temperature range of 853 to 1044 °C under C02

pressure between 2.35 and 24.89 atm. The carbonation reaction

rapidly became diffusion-controlled as CaC03 built up on the

surface of CaO. The carbonation rate was found to be a

function of the C02 pressure and temperature. The pressure

dependence was reported to follow a Langmuir-type adsorption

isotherm with the diffusion activation energy of 29 ± 6

kcal/mol.

Finally, Mess (1989) investigated product layer

diffusion in the carbonation reaction in a TGA under C02

pressure up to 12 atm over the temperature range of 550 -

1050°C using nonporous CaO particles. At high temperatures

(>900°C), the reaction rate decreased with time and was first

order in C02 concentration with respect to its equilibrium

concentration after 600 minutes. The activation energy of

steady state diffusion was reported to be 56.9 kcal/mol.

2.2 Structural Property Changes During Calcination of CaC03

As dicussed previously, calcination of CaC03-based

materials creates pores within the solid product CaO.

However, the recarbonation extent is obviously dependent upon

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the structural properties (i.e. surface area, pore volume,

and pore-size distribution) created during calcination.

In a related study, Narcida (1992) measured structural

properties resulting from the calcination and carbonation of

three calcium-based sorbents: (i) reagent grade calcium

carbonate, (ii) reagent grade calcium acetate, and (iii)

commercial dolomite. Table 2-1 summarizes the surface areas

and pore volumes of the sorbents and their precursors using

calcination conditions of 750°C in 1 atm N2 for 1 hour. The

low surface area and pore volume of the precursors illustrate

their essentially nonporous character. After calcination,

both surface area and pore volume increase significantly as

volatile components are driven from the solid. It is

interesting to note that calcium acetate precursor

experiences the greatest increase in pore volume. This is

attributed to its higher initial volatile content and the

fact that calcination occurs in three distinct steps: (i)

removal of water of hydration at 100-300°C, (ii)

decomposition of calcium acetate into calcium carbonate at

about 600°C, and finally (iii) decomposition of calcium

carbonate into calcium oxide at about 700°C.

The pore-size distributions of the three sorbents

emphasize the above results. Figures 2.2, 2.3, and 2.4

(Narcida, 1992) show the pore-size distributions of reagent

grade calcium carbonate, reagent grade calcium acetate, and

commercial dolomite, respectively, along with their calcined

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Table 2-1

Structural Properties of Test Sorbents

CaC03 Ca-Acetate Dolomite Surface Area Cm2/g) Initial 0.9 3.8 1.7 First Calcination1 18.5 23.2 14.4 First Carbonation2 1.1 3.8 6.4

Pore Volume3 (cm3/g) Initial 0.00 0.06 0.05 First Calcination1 0.25 0.96 0.40 First Carbonation2 0.00 0.15 0.15 Second Calcination 0.19 0.79 0.38

1 Calcined at 750°C, 1 atm in N2 for 1 hour

2 Carbonated at 750°C, 1 atm, 15% C02/N2 for 1 hour

3 Pore diameter range from 0.02 to 1.0 microns

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2.00

As Received

1.60 — First Calcination p

1.20

0.00 T"‘i i ITTTii 0.001 0.01 0.1 1.0 6.0 DIAMETER (MICRON)

Figure 2.2 Pore Size Distribution of As-Received Calcium Carbonate and after Calcination at 750°C in N2 Atmosphere for 1 hour (Narcida/ 1992)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. products, CaO. As shown in Figure 2.2, pores with diameters

of 0.02 - 0.08 /zm are created during the calcination of

calcium carbonate. Calcination of hydrated calcium acetate

occurs in three steps, with each step contributing to the

final structure, as shown in Figure 2.3. First, removal of

water of hydration at 3 00°C produces pores in the range of 2

- 8 /zm. Second, decomposition of calcium acetate into calcium

carbonate (shown as 550°C calcination) creates a broad

distribution of pores with a peak at 0.8 /zm. Finally, upon

decomposition of calcium carbonate into calcium oxide (shown

by the curve labeled Calcined at 750°C) two ranges of pore

sizes are formed; the larger pores cover a wide range of

diameters between 0.1 - 6 /zm and the smaller pores have an

average diameter of 0.035 /zm. The calcination of commercial

dolomite releases gaseous C02 from both MgC03 and CaC03

decomposition. As shown in Figure 2.4, this calcination

produces a bimodal pore size distribution with average

diameters of 3 /zm and 0.05 /zm, respectively.

It is interesting to note that the pores in the 0.02 -

0.08 /zm diameter range are common to all calcined precursors.

The small pores may be represented as those as being formed

during the final decomposition of CaC03 into CaO. Even though

the scales on y-axis of Figures 2.2, 2.3, and 2.4 are

different, the intensity of the 0.02 - 0.08 /zm diameter range

is essentially the same.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24

A: As Recsfved B: Calcined a t 300C C: Calcined a t 550C D: Calcined a t 750C

wn . I I .I TI I r I imllll r n n rr 0.001 0.01 1.0 6.0 DIAMETER (MICRON)

Figure 2.3 Pore Size Distribution of As-Received Calcium Acetate and after Calcination Temperatures in N2 Atmosphere (Narcida, 1992)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25

As Received

First Calcination

0.001 0.01 0.1 1.0 6.0 DIAMETER (MICRON)

Figure 2.4 Pore size Distribution of As-Received Dolomite and after Calcination at 750°C in N2 Atmosphere for 1 hour (Narcida, 1992)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26

A similar phenomenon occurs during the calcination of

CaC03 and subsequent sulfation of CaO in flue gas

desulphurization processes, which have been studied in a

great detail. As a guide to this study, important structural

effects associated with this reaction are discussed below.

Hartman et al. (1978) reported that the porosity of the

calcined CaC03 was a strong function of the porosity of the

natural rock precursors. Limestones, chalks, and marls were

tested. Subsequent sulfation results, as shown in Figure 2.5,

illustrate the importance of the calcine porosity on the

sulfation reaction. Using nonporous limestone (e^ = 0), the

fractional sulfation was less than 0.3 0 after 60 minutes. The

moderate porosity chalk (e^ = 0.27) resulted in about 0.60

to 0.70 fractional sulfation after 60 minutes, while the

calcine from the high porosity marl (e^ = 0.71) was

completely sulfated in approximately 20 minutes. Ulerich et

al. (1978) reported that the sulfation capacity of calcined

limestone was improved when calcination produced larger pore

diameters. Calcination at 900°C and 0.8 atm C02 pressure was

found to have the highest sulfation capacity.

Dogu (1981) reported that the reactivity of calcined

limestone for S02 removal increased as the calcination

temperature increased from 750 to 950°C. The improvement was

attributed to an increase in the pore size of the calcined

limestone. Zakarnitis and Sotirchos (1989) reported similar

results, and concluded that the sulfation behavior of

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0.9

o X o' uo

c o u\A % c o u a v O> jQ .

0 20 40 60 Exposure Time.t^min)

Figure 2.5 Variation of Sulfation Rate with the Porosity of Natural Rock (from Hartman et al., 1978)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28

calcined limestone particles was dependent not only on

internal surface area and porosity, but also on the pore-size

distribution and interconnectedness of the pores.

The effect of calcination conditions on the structural

properties of calcined CaC03-based materials has been

studied. For example, Borgwardt (1989) reported that the

surface area of calcined CaC03 was strongly dependent on

temperature and the presence of impurities. Fuertes et a l .

(1991) studied the changes in surface area and pore size

during the sintering of CaO samples. The presence of C02

caused a reduction in surface area and an increase in pore

size. The pore volume and porosity of CaO particles was not

affected by sintering.

2.3 Modeling of Moncatalytic Gas-Solid Reactions

A number of models analyzing the behavior of

nancatalytic gas-solid reactions have been developed. The

noncatalytic gas-solid reaction usually proceeds through the

following steps:

(i) mass transfer of gaseous reactants from the bulk gas

phase to the exterior surface of the solid particle,

(ii) diffusion of gaseous reactants through the pores of

the solid,

(iii) diffusion of gaseous reactants through the product

layer, and

(iv) chemical reaction between gas and solid reactants.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29

A brief introduction to simple gas-solid reaction models

will be presented first. Such models assume constant solid

structural properties and, therefore, are not applicable to

CaO carbonation. Variable property models which might be

applied to CaO carbonation will then be discussed.

2.3.1 Unreacted Core Model

The unreacted core model (Yagi and Kunii, 1955) is the

simplest of the gas-solid reaction models. It assumes that

the reaction occurs at a sharp interface between the solid

reactant and product. Initially the interface is at the outer

surface of the solid, but as the reaction progresses, the

interface moves into the interior leaving behind a completely

reacted product layer (see Figure 2.6). This model is limited

to systems in which the solid reactant is nonporous or for

the cases in which internal diffusion controls the reaction

rate. It is interesting to note that the unreacted core model

equations have an analytical solution making it possible to

analyze the effects of the individual resistances.

2.3.2 Volumetric Model

The volumetric, or homogeneous model, describes gas-

solid reaction systems in which the reaction occurs

homogeneously throughout the solid (Ausman and Watson, 1962;

Wen, 1968). This behavior occurs in highly porous solids

where the chemical reaction resistance is much greater than

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

u o rgnl Concentration Original r o High Conversion High r h Front Time Reaction Core Unreacted r o Radial Position r Product or Ash Time Figure 2.6 Schematic of the unreacted core model Low Conversion Low cCC cCC s 8 s | 0 1 § 1

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the resistance due to internal diffusion. Figure 2.7 shows a

schematic diagram of the model. In contrast with the

unreacted core model, the volumetric model equations require

numerical solution of the gas phase and solid phase material

balances to obtain the time-conversion relationship.

2.3.3 Constant Property Grain Models

Grain models assume that the reacting solid consists of

a matrix of very small grains (see Figure 2.8). The space

between the grains constitutes the porous network. The model

assumes that the overall grain sizes remain constant during

the reaction. The reactant gas is transported to the surface

of the particle from the bulk gas stream, diffuses between

the grains, then through the solid product layer surrounding

each grain, and reacts at the reaction interface. The

reaction takes place within the grain according to the

unreacted core model. These models were extensively developed

by Szekely and coworkers (Szekely and Evans, 1970, 1971; Sohn

and Szekely, 1972; Szekely et al., 1973).

2.3.4 Constant Property Pore Model

Szekely and Evans (1970) also proposed a constant

property pore model. The reacting solid is considered to be

semi-infinite containing pores of uniform radius (see Figures

2.9a and 2.9b). The gaseous concentration is assumed to be

constant at the mouth of the pore. The reactant gas diffuses

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

to rgnl Concentration Original r, o r, High Conversion High Time r. o S r, Radial Position Time Figure 2.7 Schematic of the Volumetric Model 48 Low Conversion Low

<8 £ £ § c

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. to U> Original Concentration Radial Position High Conversion High Time \ ° 1 ° ° / ° ° Solid Product o oo oo o oo o •o o •o o •o o • •• O O O 0 o • •o o oo o • • Solid Unreacted r, Figure 2.8 Schematic of the grain model o Radial Position Low Conversion Low Ti

c c § £ © 2 8 o ° ££C •2 t> •2 Ow

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/ftaf

Soto

y-0

Figure 2.9a Schematic Representation of the Pore Model

(From Szekely and Evans, 1970)

Unreacted Solid

yS.flroducKZ Solip A ! Free Surface

Figure 2.9b The Reaction Front in the Pore Model

(From Szekely and Evans, 1970)

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axially through the pore and initially reacts with solid at

the pore wall. Subsequently, a solid product layer is formed

and, consequently, reactant gas must diffuse radially through

this product layer. This causes the thickness of the product

layer to be greater near the pore mouth (free surface) as

shown in Figure 2.9b.

2.4 Modeling of Moncatalytic Gas-Solid Reactions with

Structural Property Changes

In noncatalytic gas-solid reactions, when the molar

volume of solid product is greater or smaller than the molar

volume of solid reactant, the structural properties of the

solid are expected to change. For example, for the reaction

of current interest, the solid reactant CaO, having a molar

volume of 16.8 cm3/g, reacts with gaseous C02 to produce solid

CaC03 having a molar volume of 36.9 cm3/g. Depending upon the

initial solid structure, the reaction may cease well below

the theoretical maximum conversion as a result of the

structural changes during the reaction.

A number of models to describe noncatalytic gas-solid

reactions undergoing structural property changes have been

developed, and the models may be classified into two groups:

grain models and pore models.

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2.4.1 Grain Models with Structural Changes

Hartman and Coughlin (1976) modified the constant

property grain model in describing the sulfation of CaO. The

pellet porosity was considered to decrease as the reaction

proceeded. This caused the gas diffusion resistance within

the pellet to increase. The model did predict the reaction

"die-off" as observed experimentally (Hartman and Coughlin,

1974) .

Georgakis et al.(1979) also modified the grain model by

considering changes in the porosity of the pellet during the

reaction. The porosity changes were attributed to the

formation of a product layer on the grains which caused the

grain diameter to increase as a result of differences in the

molar volumes of reactant and product solids.

Ranade and Harrison (1979, 1981) developed the modified

grain model to account for structural changes due to

sintering and chemical reaction. Figure 2.10a illustrates the

initial condition of grains, while Figure 10.2b illustrates

the sintering which occurs during the reaction. The solid

reactant was assumed spherical and was composed of

microscopic spherical grains which reacted according to the

unreacted core model. During the course of reaction, the

specific surface area of the pellet and the grain density

changed causing the change in grain radius. Sintering caused

the adjacent grains to combine (see Figure 2.10b), thereby

increasing the size of the grains and reducing their number.

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*o 'c ' «„

(a) INITIAL CONDITIONS

Time Time

(b) SINTERING

Figure 2.10 Modified Grain Model with Structural Changes Due to Sintering and Chemical Reaction (Ranade and Harrison, 1979)

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Significant improvement was achieved in matching the

experimental data for the reaction between H2S and ZnO as

compared to the constant property grain model.

Sotirchos and Yu (1988) developed a structural model by

allowing grains to overlap. The porous solid was represented

by a population of randomly overlapping grains of distributed

size which react according to a shrinking core model.

2.4.2 Fore Models with Structural Changes

Ramachandran and Smith (1977) developed a single pore

model for predicting the conversion-time relationship for

noncatalytic gas-solid reactions. The model focused on the

structural changes taking place in a single pore which was

representative of the changes in the pellet. Figure 2.10

shows a cyclindrical pore of initial radius r. The single

pore has a length 1 , and the solid reactant associated with

that pore has an overall radius X. The model considers the

influence of pore diffusion, diffusion through the product

layer, and surface reaction. When a significant gas

concentration gradient along the pore exists (i.e. pore

diffusion is an important resistance), a product layer of

thickness (6l+S2) , as shown in Figure 2.11 is formed at

position x. 5, and S2 are maximum at the pore mouth, x = 0.

Consequently, the reaction can be stopped before complete

conversion due to pore plugging at the mouth of the pore.

The model was applied to the experimental conversion-time

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pore product

reactant

Figure 2.11 Geometrical View of Single Pore Model (From Ramachandran and Smith, 1977)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40

data by Hartman and Coughlin (1974) . There was good agreement

between the model and experiment at the early stages, but the

model overpredicted conversion as the reaction time

increased.

Chrostowski and Georgakis (1978) independently developed

a single pore model similar to that of Ramachandran and Smith

(1977). The model considered effective diffusion coefficient

(combination of molecular and Knudsen diffusion coefficients)

changes due to the decrease in pore size as the product layer

built up during the reaction. The model was, however, not

able to improve the quantitative agreement to the

experimental data of Hartman and Coughlin (1974). Lee (1980)

analyzed the single pore model for a parallel-plate pore. The

model was simplified to produce an analytical solution

between conversion and time. Shankar and Yortsos (1983) also

simplified the single pore model and obtained an asymptotic

solution. The model was applied for large values of the

Thiele modulus corresponding to pore diffusion control or

narrow pores.

Bhatia and Perlmutter (1980, 1981) developed a so-called

random pore model which allowed for variation of pore

structure during the reaction. The model introduced a

structural parameter which was a function of the type of pore

size distribution. Pore overlapping was allowed to occur. The

model was applied to CaO sulfation (Bhatia and Perlmutter,

1981) and carbonation of CaO (Bhatia and Perlmutter, 1983) .

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41

A similar model was developed independently by Gavalas

(1980).

Sotirchos and Yu (1985) developed a structural model for

gas-solid reactions with solid product which allowed pore

closure. The model considered the effect of pore overlap on

diffusion in the product layer and on the evolution of the

pore surface and of the solid product-reactant interface, but

did not allow for formation of inaccessible pore space. The

pore structure was represented as a population of infinitely

long cylindrical capillaries. Yu and Sotirchos (1987) then

extended the model to allow the formation of inaccessible

pore space by considering pore structures as a network of

finite cylindrical capillaries. Percolation theory was used

to describe the formation of inaccessible pores.

The grain and pore models discussed above were developed

by considering the solid structure to have an average grain

or pore size. Christman and Edgar (1983) developed a so-

called distributed pore size model to describe the evolution

of pore size distribution as the reaction occurred by using

population balance techniques. The model accounted for four

resistances to the overall reaction: mass transfer of

reactive gas into the pellet, pore diffusion within the

pellet, product layer diffusion, and surface reaction. A

detailed explanation of this model will be presented in

Chapter 8 .

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42

Sahimi et al. (1990) recently reviewed the noncatalytic

gas-solid reaction models. They emphasized the use of

percolation theory to account for the effect of dead ends,

tortuous paths, and the interconnectivity of the pores.

Yortsos and Sharma (1986), Reyes and Jensen (1987), and Yu

and Sotirchos (1987) developed percolation-based models for

describing the incomplete reactions which occur in

noncatalytic gas-solid reactions.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3

Experimental Apparatus and Procedure

The equipment and procedure used to collect experimental

data in this research are described in this chapter. First,

the atmospheric pressure electrobalance used for preliminary

studies is presented. Second, the high pressure

electrobalance reactor system will be described along with

experimental difficulties encountered when using water vapor

at high pressure in the electrobalance. The modification to

the reactor vessel to overcome the problem is also presented.

A description of materials and the gas delivery systems will

follow. Finally, the procedure followed during a typical run

using the high pressure electrobance is described.

3.1 Atmospheric Thermogravimetric Analyzer

An atmospheric pressure electrobalance reactor system

was used during preliminary screening studies to compare the

performance of different sorbents and determine appropriate

calcination and carbonation temperatures. Figure 3.1 shows a

diagram of the atmospheric pressure electrobalance system.

The system consists of a Cahn 2 000 Electrobalance equipped

with a temperature programmer/controller (MicRicon), a

Bascom-Turner 113-DC data center, and a gas flow control

center. All gases were obtained from high purity cylinders

and the flows were regulated by calibrated rotameters. Inert

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44

Balance Mechanism Electrobalance Inert Control Gases Unit

Reactive Gases

Reactor

Thermocouple

MicRlcon Bascom Turner Temperature Model 113-DC Programmer/ Data Controller Center

Condenser

Figure 3.1 Schematic of the Atmospheric Pressure Electrobalance System

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45

gas was added through the upper flow path to blanket the

balance mechanism and prevent corrosive gas from reaching the

balance mechanism. Additional inert and reactive gases were

premixed and entered the reactor through the side arm of the

hangdown tube. The combined gases flowed downward over the

sample, passed through a condenser, and were vented to a

laboratory hood. Water was introduced to the reactive gas

stream using a Harvard Apparatus Model 944 precision syringe

pump. To induce water vaporation, the line was heated at the

point where water mixed with the reactive gases. The reactive

gas feed line was also heated until it reached the reaction

furnace to prevent water condensation.

Reaction temperature was monitored using a chromel-

alumel thermocouple positioned about % inch below the sample

container. The thermocouple signal was transmitted to the

MicRicon temperature programmer/controller. The thermocouple

signal and the sample mass signal from the electrobalance

were transmitted to the Bascom-Turner data system where

results were stored on diskette and/or plotted on an x-y

plotter.

A typical atmospheric pressure electrobalance response

curve for one complete calcination and carbonation is shown

in Figure 3.2. The sample was heated at 50°C/min to 750°C.

Initial calcination, corresponding to the solid weight loss,

was observed at a temperature of about 725°C, and calcination

was complete approximately 30 minutes after the final

DIMENStONLESS WEIGHT, W/Wo 0.60 0.80 1.00 0 20 abnto:60, 6XC02/ 1 atm ,1 2 /N 2 0 C X .6 5 630C, Carbonation: 750C, Calcination: ) 1 -9 (R 1 Sorbent 40 IE MIN. TIME, 080 60 N2,1 atm

100 120 -200 -400 -600 800

TEMPERATURE, C 46 47

temperature of 750°C was reached. The sample weight at the

end of the calcination cycle was equal to the theoretical

value of W/Wo = 0.56 which corresponds to the complete

conversion of CaC03 to CaO. Temperature was then adjusted to

630 °C and the recarbonation phase was initiated by

introducing 5.6% (vol) C02 in N2. The rate of recarbonation

was quite rapid for two minutes to W/Wo = 0.84. Thereafter

the recarbonation rate became slow and the final W/Wo value

was only about 0.86 when the run was terminated 35 minutes

after carbonation began.

3.2 High Pressure Electrobalance Reactor System

The high pressure electrobalance reactor system is the

primary equipment used in this research. Figure 3.3 shows a

diagram of this reactor system which consists of a Cahn Model

1100 high pressure balance and its balance mechanism housing,

a Cahn Model 1000 electrobalance controller, a gas feed

system, and a furnace housing.

The Cahn pressure balance model C-1100 is the key

component of the system. The housing and hangdown tube are

constructed of 316 stainless steel capable of operating up to

1500 psi at 600°C. Two black anodized spacers are inserted in

the balance mechanism housing to minimize dead volume. The

balance is connected to the Cahn Model 1000 electrobalance

controller having 100 g capacity and 10 jug sensivity. The

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 00

r or L i 2 I I CO/H? C0/H„/H~S

CO,

N2 o - Z T - n — CV MFC CV MFC F

CV CV MFC F ^ - 9 -

F - Filter V - Valve PI - Pressure Indicotor SV - Surge Volume CV - Check Valve TC - Thermocouple f BPR - BocK Pressure Regulator PRV - Pressure Relief Volve MFC - Moss Flow Controller CONO CONO - Condenser SYRINGE c v MFC VAJ-VE VAJ-VE PUMP VALVE 3-WAY 3-WAY VALVE COND Figure 3.3 Schematic Diagram of High Pressure TGA FURNACE COND

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49

Table 3-1

Cahn 1000 Performance Specifications

Capacity 100 g

Mechanical Tare 100 g

Electrical Tare 10 g

Sensitivity 1 Mg

Repeatability 10E-5 of total load on both pans

Ultimate Repeatability 1.5 Mg

Temperature Stability Between 20 and 26°C

Recorder Zero Agreement

Between Ranges 0.5% of Range

Calibration Range Agreement: 0.2% of Range

Linearity 0.025% of Range

Accuracy 0.1% of Meter and Recorder Range

(MRR) + 1.5E-4 of Weight

Suppression Range (WSR)

Maximum Weight Change 10 g

Bakeout Temperature 125°C maximum

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50

specifications of the Cahn Model 1000 electrobalance are

illustrated in Table 3-1.

The solid sample was placed on a 9 mm-diameter bowl-type

platinum container which was suspended inside the reactor

hangdown tube from the electrobalance using a nichrome

hangdown wire. Temperature measurement was provided by a K-

type thermocouple placed about 1% inch directly below the

sample container. The reactor temperature was maintained

using a single zone split-tube furnace (Applied Test System

Series 3210) equipped with a single zone temperature

controller (Model 2010) and CFE Model 2040 limit controller.

The temperature controller is microprocessor programmable

with capability of up to 8 ramp-and-soak intervals and up to

254 cycles. The limit controller is designed to shut down the

furnace system when the furnace temperature exceeds 1000°C.

The feed gas system consists of N2 gas to the balance

mechanism housing, and N2, C02, and CO/H2 or CO/H2/H2S gases to

the side arm of the hangdown tube. Each gas is fed from a

high pressure cylinder through a gas filter, a high pressure

mass flow controller (Porter Instrument Model 201), and a

check valve. Water vapor is generated by supplying water from

a high pressure syringe pump (Harvard Apparatus Model 909).

The feed line leading to the side arm of the reactor hangdown

tube is heated to induce water vaporation. A surge volume

consisting of a 3 00 ml high pressure sampling bomb is

included in the syringe pump exit line to dampen steam flow

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51

variations. Combined gases flow downward over the solid

reactant and exit from the bottom of the hangdown tube.

Exit gases pass through a condenser immersed in an ice

bath followed by a filter, and are vented either through a

three-way valve for atmospheric pressure runs or through a

back-pressure regulator for high pressure runs. An identical

condenser and filter arrangement is provided in the side arm

gas feed line so that flow rate, composition, and pressure

may be adjusted while reactant gas bypasses the reactor.

Data of solid sample weight, reactor temperature, and

furnace temperature are acquired using an IBM PC with a 286

processor. A data interface package and software (supplied by

Laboratory Technologies Corporation) were used for data

acquisition and processing.

A typical electrobalance response curve through one

complete calcination and carbonation cycle using reagent

grade CaC03 (Sorbent 1) is shown in Figure 3.4. 11.8 mg of

CaC03 were heated at a rate of approximately 5° C/minute to

750°C in N2 at 1 atm. Due to the large reactor tube mass, a

nonlinear response occured for the first 50 minutes of the

heating cycle. However, the heating rate approached

linearity before the calcination began.

The sample weight showed a small apparent increase

during the early heating period prior to the beginning of

calcination. This apparent weight increase was due to

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1,000 Sorbent 1 (HP026) Calcination: N2,1 atm Carbonation: 1 5 IC 0 2 /N 2 ,5 atjn 800

o 600

•400 TEMPERATURE, C TEMPERATURE,

200

0 SO 100 150 200 250 300 TIME, MIN.

Figure 3.4 Typical High Pressure Response

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53

increased aerodynamic drag exerted by the flowing N2 as the

temperature increased.

Calcination began after 125 minutes at the temperature

of approximately 650°C and was complete after 150 minutes

when the temperature reached 750°C. The sample weight of 6.6

mg at the end of calcination corresponds to the theoretical

weight associated with the complete decomposition of pure

CaC03 to CaO (44% weight loss).

After 180 minutes, the reactor pressure was increased to

5 atm of N2 in preparation for carbonation. As shown in

Figure 3.4, pressurization produced a temporary upset in the

measured sample weight. Once the final pressure of 5 atm was

reached, the sample weight stabilized at 6.6 mg. After 210

minutes, the reactive gas composed of 15%C02 in N2 was

introduced to the reactor tube. The carbonation reaction

began immediately as indicated by the solid weight increase

to 10.5 mg within approximately two minutes. Thereafter, the

rate became quite slow and a maximum weight of 11.0 mg was

reached when the run was terminated after 280 minutes. The

10.5 and 11.0 mg weights correspond to fractional

carbonations of 0.75 and 0.85, respectively. These typical

results are consistent with previous results reported in the

literature (Barker, 1973, 1974; Bhatia and Perlmutter, 1983).

The high pressure reactor system described above worked

well in runs at all pressures when no H20 was included in the

carbonation gas. In addition, no experimental problems were

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54

encountered using H20 at atmospheric pressure. However,

severe experimental problems were found when high pressure

carbonation runs with steam in the carbonation gas were

attempted.

A typical electrobalance response during the carbonation

cycle of a run in which 10% steam was introduced at 5 atm is

shown in Figure 3.5. For approximately 3 0 minutes,

carbonation proceeded in a normal manner; rapid initial

reaction was followed by the expected abrupt transition to

the very slow reaction after 5 minutes. At about 30 minutes,

however, an abrupt solid weight loss of about 4 mg was

recorded. Five minutes later, another 4 mg of solid was lost.

The run was terminated after two additional weight losses

occured. Only about 0.5 mg of sorbent remained in the sample

pan. The actual solid loss was confirmed after the reactor

was cooled and opened for inspection.

Steam condensation on the inside of the reactor hangdown

tube in the cool zone where the hang-down tube joined the

balance housing was believed to be the cause of the problem.

During the carbonation phase using steam, the reactive gas

gradually diffused upward to the cool zone when water vapor

condensed and fell periodically into the hot zone where

almost instantaneous vaporization occured. This produced a

pressure wave of sufficient magnitude to dislodge solid from

the sample pan. The problem was not encountered in

atmospheric pressure runs since the volumetric flow rate of

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sorbent 9 (HP174) Calcination: 750C, N2,5 atm Carbonation: 750C, 15X C 02/10X H 20/N 2,5 atn? n r 20 TIME, MIN.

Figure 3.5 Typical Response using Water Vapor

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56

inert gas through the balance housing was sufficient to

prevent steam from diffusing upward to the cool zone. At

elevated pressures, the volumetric flow rate of inert gas was

insufficient to prevent back diffusion of steam.

The above problem was solved by machining a close-

fitting stainless steel rod which was inserted into the upper

portion of the hangdown tube where it joined the balance

housing. A diagram of the hangdown tube with insert is shown

in Figure 3.6. The upper portion of the insert was attached

by a press fit to the flange which attaches to the balance

housing. The hang-down tube fit over the insert and the

teflon sleeve sealed against the walls of the hang-down tube

to prevent steam from reaching the upper cooler sections. A

small hole was drilled through the wall of the insert to

allow pressure equalization above and below the teflon

sleeve.

Several runs were attempted after modification of the

hangdown tube. There was no evidence of dislodging the sample

from the sample pan. It was discovered, however, that a small

amount of water condensation along the hangdown wire in the

cooler regions was still occuring. While the amount of

condensate was quite small and no droplets were formed, the

condensate produced a small increase in apparent sample

weight, thereby causing an error in the kinetic results. The

open area of the gas outlet from the insert tube was reduced

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57

O - Ring

Flange

O - Ring

Pressure Equalization

Stainless Steel Insert

Teflon Sleeve

Reactive Gas Entrance

Figure 3.6 Diagram of the Insert Added to the Hangdown Tube to Prevent Steam Condensation

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58

to prevent steam from back-diffusing up the insert (see

Figure 3.6). No further experimental problems were

encountered.

Figure 3.7 compares the results of a run using the

original insert with the larger opening with results of a run

after reducing the diameter of the opening. The insert having

the larger opening was used in run HP193; a small but steady

weight gain in the 5 to 22 minute time span is evident. At 22

minutes, the reactive gas (including steam) flow was stopped

in preparation for the second calcination cycle. An apparent

weight loss caused by evaporation of water from the hang-down

tube resulted. In Run HP205, the inside diameter of the

opening was reduced and there was essentially no weight gain

in the 5 to 25 minute time span. Reactive gases were stopped

after 25 minutes and no weight loss occured. Indeed, after 35

minutes the sample weights were effectively the same in both

runs. The second calcination cycle was initiated after about

40 minutes, and the calcination curves for both runs were

effectively identical.

3.3 Materials

Gases were obtained from high purity gas cylinders. In

most runs nitrogen (99.96% purity), carbon dioxide (99.9%

purity), and a mixture consisting of 67.3%CO/32.7%H2 were

used. A mixture of 32%H2, 65%CO, and 3%H2S was used in a

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59

Sorbent 9 Calcination: 750C, N2,1 atm Carbonation: 750C, 15XC02/10XH20/N2,15 atm o 0 .8 0 ' 5 □ HP193 □ lA a HP205 0.70* f

I SQ.60H ;

0.50- - f ■ I- - 1 ■■■ "i" 20 40 60 80 TIME, MIN.

Figure 3.'7 TGA Response Using Water Vapor

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limited number of tests to determine the effect of H2S on the

carbonation reaction.

A total of nine calcium-based sorbent precursors were

used in preliminary studies. Table 3-2 presents a general

description of the sorbents. Reagent-grade calcium carbonate

(sorbent 1) , calcium acetate (sorbent 7), and calcium sulfate

(sorbent 8) were supplied by Mallinckrodt Chemicals.

Sorbents 2 through 6 were all commercial-grade CaC03 obtained

from producing quarries. Commercial dolomite (sorbent 9)

contained approximately equal molar quantity of MgC03 and

CaC03.

As a result of preliminary screening tests, sorbents 1,

7, and 9 were selected for detailed studies. The complete

chemical analysis of these materials is presented in Tables

3-3, 3-4, and 3-5.

All commercial sorbents were received as relatively

large chunks. These materials were oven dried for 24 hours,

crushed in a mortar, and then screened with the -400 mesh (<

38 //m diameter) fraction used in reaction tests. The reagent

grade materials were in fine powder form. These materials

were sieved directly and the -400 mesh fraction used in

reaction tests.

3.4 Experimental Procedure Using High Pressure Electrobalance

Approximately 12 mg. of sorbent precursor was added to

the sample pan and suspended on the hangdown wire from the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 3-2

Description of Calcium-Based Sorbent Precursors

Sorbent General Description Source

1 Reagent grade calcium Mallinckrodt Chemicals carbonate, CaC03

2 Marl from producing Gifford-Hill Co. quarry Harleyville, SC

3 Chalk from producing United Cement Co. quarry Artesia, MS

4 Chalk from producing Texas Crushed quarry Stone Co. Georgetown, TX

5 Limestone from newly Vulcan Materials developed quarry in Co., Houston, TX Yucatan, Mexico

6 Chalk from producing Gifford-Hill Co. quarry Midlothian, TX

7 Reagent grade calcium Mallinckrodt Chemicals acetate, Ca (C2H3O2) 2 • x H2O

8 Reagent grade calcium Mallinckrodt Chemicals sulfate, CaS04. 2 H20

9 Dolomite, CaC03.MgC03 National Lime Co. Findley, OH

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62

Table 3-3

Chemical Analysis of Reagent Grade CaC03 (as Reported by Mallinckrodt)

CaC03 99.97% (after 2 hours at 285°C)

Alkalinity Passes Test

Ammonium (NH4) 0 .002%

Barium (Ba) 0 .002%

Chloride (Cl) 0 .001%

Fluoride (F) 0.0009%

Heavy Metals (as Pb) 0.0005%

Insoluble in HC1 and NH4OH ppt 0.00025%

Iron (Fe) < 0 .0002%

Magnesium (Mg) 0.0006%

Other Alkalis Passes test

Oxidizing Substances (as N03) < 0.005%

Potassium (K) 0.0006%

Silica (Si02) < 0.0006%

Silicon (Si) 0.0003%

Sodium (Na) 0 .002%

Strontium (Sr) 0.006%

Sulfate (S04) < 0.0025%

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 3-4

Chemical Analysis of Reagent Grade Calcium Acetate (as Reported by Mallinckrodt)

Ca(C2H302)2 > 91.47%

Barium (Ba) < 0.005%

Chloride (Cl) < 0.001%

Heavy Metals (as Pb) < 0.001%

Iron (Fe) < 0.001%

Magnesium and Alkali Salts < 0.2%

Sulfate (S04) < 0.01%

Water 8.3%

Table 3-5 Chemical Analysis of Dolomite (as Reported by National Lime Co., Findley, OH)

Component Weight %

CaC03 54.5

MgC03 45.0

Si02 0.2

F e203 0.07

A 1203 0.08

S 0.03

Other 0.12

Loss on Ignition after Calcination at 1800°F - 47,

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balance. N2 from a high pressure cylinder was fed using a

mass flow controller adjusted at 2 liter/min to build up the

desired operating pressure in the reactor system. The

pressure was controlled using a back pressure regulator.

During this time, the gas line was heated to insure

vaporation of water. The liquid water flow rate from the high

pressure syringe pump was adjusted and checked by bypassing

the water flow to a graduated cylinder. After the temperature

along the gas feed line was steady, the water was switched to

mix with the reactive gases. After about 15 minutes, the

reactive gas line was switched to a back pressure regulator

to build up the same pressure as the reactor system. The

total flow rate of reactive gases was 200 ml/min (STP).

After the reactor system reached the appropriate

pressure, the N2 gas flow rate to the balance housing was

reduced to 300 ml/min (STP). About 10 minutes later, power

was supplied to the furnace to initiate heating at a rate of

approximately 5°C/minute.

The sample weight and temperature were monitored during

the heating period. Approximately 30 minutes after

calcination was complete, the reactive gases were introduced

to the reactor to initiate the carbonation reaction. At the

end of carbonation cycle, the power supply to the furnace was

shut off and the reactor was depressurized by very slowly

switching the 3-way valve to the atmosphere. The water supply

from high pressure syringe pump was immediately stopped.

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After the reactor cooled to about 400°C, a temperature at

which calcination would not occur, the reactive gas flow rate

was stopped. N2 flow through the reactive gas line was

maintained for sufficient time to purge the reaction gases.

About 10 minutes later, the N2 gas flow rate to the balance

housing and through the side-arm was reduced to about 20

ml/min.

After the reactor reached room temperature, the sample

container was unloaded, weighed using a Sartorius balance,

and cleaned. The empty pan was again loaded to the balance to

measure the empty-pan weight for comparison to the weight

before the run.

The experimental procedure described above was followed

for one complete calcination and carbonation cycle with the

same operating pressure for both phases. If the calcination

phase was at atmospheric pressure and carbonation phase was

at elevated pressure (see Figure 3.2), the reactor system was

pressurized after the calcination was complete with the

procedure similar to that described above.

Many of the experimental tests using the high pressure

electrobalance system were continued for several cycles. The

experimental procedure was similar but involved additional

switching of reactive gases between reactor and the by-pass

lines between the calcination and carbonation cycles.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 4

Experimental Results:

Reaction Screening Tests

This chapter deals with the preliminary studies which

investigated the effect of operating conditions as well as

screened potential sorbent precursors. Operating conditions

included the effect of calcination temperature, carbonation

temperature, and background gas composition. Reagent grade

CaC03 was used in these tests. The results of these tests

suggested the operating conditions which were used for

screening of sorbent precursors. Three out of nine sorbent

precursors were selected for further kinetic studies. They

were: (i) reagent grade CaC03 considered as a standard

sorbent, (ii) reagent grade calcium acetate, and (iii)

commercial grade dolomite having essentially equal molar

quantities of MgC03 and CaC03.

The preliminary studies used the atmospheric pressure

thermogravimetric analyzer while the high pressure TGA was

being acquired. It is necessary, however, to point out that

the atmospheric pressure TGA experienced a problem in

temperature measurement. The actual temperature was about 20

to 30°C below the temperature reading from the temperature

controller. Since this effort was only for preliminary

studies, the temperature problem did not significantly affect

the preliminary analysis. In addition, the preliminary

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67

results were excluded in detailed studies discussed in the

next chapters. Controller temperature is reported in the

following.

4.1 Effect of Temperature

Figure 4.1 shows the effect of temperature on the

calcination reaction. Calcination was carried out in N2 at 1

atm using a heating rate of 50°C/minute to the indicated

temperature and isothermal thereafter. The calcination rate

is a strong function of temperature. Calcination was very

slow at 600°C, and the rate increased with temperature.

Calcination was complete after about 25 minutes at 845°C and

after about 200 minutes (not shown) at 660°C. These results

showed that complete calcination could be achieved in a

relatively short time at temperatures as low as 710°C.

The effect of carbonation temperature is shown in Figure

4.2. All sorbents were previously calcined at 750°C in 1 atm

of N2. Carbonation was at 1 atm in 5.6% C02/N2. Each run

showed the typical initial rapid reaction phase followed by

an abrupt change to a slow reaction phase, in agreement with

previous results reported in literature (Dedman and Owen,

1962; Barker, 1973, 1974; Bhatia and Perlmutter, 1983). It

can also be seen that the end of the rapid carbonation phase

is a strong function of temperature suggesting that the rate

was controlled by the diffusion of gas into the product layer

of CaC03. The final fractional carbonations at 430°C and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68

Sorbent 1 Calcination: N 2,1 atm Heating Rate: 50C /m in.

r "t '"i ■" ■" 20 30 TIME, MiN.

Figure 4.1 Effect of Temperature on Calcination Kinetics; Sorbent l

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69

Sotrbonl 1 C d c M o n : 750 C, N 2 ,1 atm 1.00- Carbonation: 5 .6 Z C 0 2 /N 2 ,1 aim

630C (R—74)

0 .8 0 -

^ 530C (R—76)

430C (R—77)

0 2 4 6 8 10 TIME, MIN.

Figure 4.2 Effect of Temperature on Carbonation Kinetics: Sorbent l

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70

750°C were 0.16 and 0.75, respectively. The global rate

during the rapid reaction phase was approximately equal in

the temperature range 430 to 680°C, and the decrease in the

global reaction rate at 750°C can be attributed to the fact

that the actual partial pressure of C02 was only slightly

greater that the equilibrium partial pressure at this

temperature.

Figure 4.3 shows the carbonation reaction behavior in a

test extended to 24 hours. Calcination was carried out at

895°C in 1 atm of N2 followed by carbonation at 710°C in 15%

C02/N2. The rapid reaction phase ended at W/Wo = 0.85,

corresponding to fractional carbonation of 0.66. After 24

hours, W/Wo gradually increased from 0.85 to 0.93 (84%

carbonation). This test showed that the carbonation reaction

never stopped completely.

4.2 The Effect of Gas Composition

The effect of C02 concentration on the carbonation

reaction is shown in Figure 4.4. The reactive gases consisted

of C02 and N2 only. An expected strong dependence of

carbonation rate during the initial rapid reaction phase was

confirmed. However, there was relatively little difference in

the carbonation level at the end of the run.

The effect of background gas components, CO and H2, is

shown in Figure 4.5. This gas composition includes all major

components present in coal-gas except steam. The addition of

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sorbent 1 (R-17) Calcination: 895 C, N 2 ,1 atm Carbonation: 710 C, 15ZC02/N2,1 atm

0.60

0 5 10 15 20 25 TIME, HRS.

Figure 4.3 Long-Term Carbonation Results; Sorbent l

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72

Sorbent 1 Calcination: 750 C, M2,1 atm Carbonation: 630 C, t atm

15XC02/N2 (R

5.56ZC02/N2 (R-74)

20 40 60 80 100 120 140 160 TIME, SEC.

Figure 4.4 Effect of C02 Concentration on Carbonation Kinetics; Sorbent 1

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73

Sorbent 1 Calcination: 750 C, N 2 ,1 atm 1.00' Carbonation: 750 C, 1 atm

5.56XC02/N2 (R-100)

0.80' 5.56ZC02/1 0ZH2/21ZC0/N2 (R-117)

0.60'

10 TIME, MIN.

Figure 4.5 Effect of Gas Composition on Carbonation Kinetics Addition of CO and H2, Sorbent l

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74

CO and H2 appears to result in a slight decrease in the rapid

reaction rate, but the rapid reaction period ends at

essentially the same level of W/Wo.

The addition of steam to complete the simulated coal-gas

composition produced a dramatic increase in the carbonation

rate during the rapid reaction phase as shown in Figure 4.6.

Two possible reasons for the rate increase were considered.

First, since all components required for the water-gas shift

reaction were present, the occurrence of this reaction would

increase the C02 concentration above that of the feed gas;

hence the rate during the rapid reaction phase would

increase. Second, H20 might simply serve to enhance the rate

of the rapid reaction phase. In order to help distinguish

between these possibilities, an additional run in which the

reaction gas consisted of 8.9% C02 in N2 was carried out.

Calculations showed that if the simulated coal gas feed was

allowed to be in shift equilibrium, the C02 composition would

be increased to approximately 9%. As shown in Figure 4.6, the

rates for the two tests were approximately equal. While the

evidence is indirect, there is the suggestion that the shift

reaction occurs simultaneously with carbonation when the

necessary shift components are present.

Other evidence of the occurrence of the shift reaction

is shown in Figure 4.7. In run R-134, the C02 feed

concentration was held constant while the background gas

composition was changed ten minutes into the run. Initially

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sorbont 1 Coleinatiof): 750 C, N 2 ,1 atm 1.00- Carbonation: 750 C, 1 atm

8.9XC02/N2 (R-142)

52C02/55XC0/27ZH2/8XH20/N2 (R-128)

52C02/N2 (R-130)

10 15 20 TIME, MIN.

Figure 4.6 Testing for the presence of the Shift Reaction Sorbent 1

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Sorbent 1 T Calcination: 750 C, N 2 ,1 dim 1.00" Carbonation: 750 C, 1 atm

0.80-

0.60 5XC02/27ZH2/N2 (R-1

10 TIME, ION.

Figure 4.7 carbonation Kinetics with Constant C02 Concentration and Varying Background Gas Composition; Sorbent l

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77

the feed gas consisted of 5%C02/27%H2/68%N2, and no

carbonation occurred. This gas composition included the

components (H2 and C02) for the reverse shift reaction which

would result in an equilibrated gas composition below

equilibrium C02 pressure for the carbonation reaction. After

10 minutes, H20 was substituted for H2 to prevent the reverse

shift reaction. Carbonation began immediately and proceeded

to a W/Wo value approximately equal to that observed using

the simple C02/N2 composition.

Results of one final test (R-144) showing the importance

of background gas composition are shown in Figure 4.8. The

feed gas contained no C02 but did contain the shift reactants

CO and H20. The observed weight increase proves that

carbonation did occur, and the only reasonable source of C02

was from the shift reaction. Carbonation was transitory,

however, as the W/Wo value reached a maximum of approximately

0.68 after 10 minutes and declined thereafter. This behavior

is consistent with CaO serving as a shift catalyst. Early in

the test when most of the sorbent was in the oxide form, the

shift reaction produced C02 which subsequently reacted to

form CaC03. Once an appreciable quantity of CaC03 was formed,

the catalytic effect diminished, less C02 was formed, and

CaC03 began to decompose.

The evidence of the water gas shift reaction combined

with C02 removal in the presence of CaO sorbent observed in

this preliminary study was indirect. In order to obtain

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Sorbtnt 1 Cokination: 750 C, N 2 ,1 atm 1.00 Carbonate 750 C, 1 atm

5ZC 02/N 2 (R—130)

0.80

55ZC0/272H2/8ZH20/N2 (R-144)

0.60

0 10 20 30 40 50 TIME, INN.

Figure 4.8 Carbonation with No C02 in the Feed Gas; Sorbent 1

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79

direct evidence of the occurrence of the water-gas shift

reaction, a more detailed study involving gas analysis will

be necessary. It will also be important to determine whether

the shift reaction is homogeneous or is catalyzed by solid

CaO. A number of metals and metal oxides are reported to be

active shift catalysts (see, for example, Rofer-DePoorter,

1984). CaO, however, is not included. Gauthier (1909)

reported that the shift reaction could occur homogeneously at

conditions of interest in this study. Gluud et a l . (1931)

reported that MgO had a catalytic effect on the shift

reaction.

The combined reactions, however, create problems for the

current study in that the C02 concentration in contact with

the CaO sorbents is not equal to the feed gas composition

whenever shift reaction components are present. Therefore,

the simple reactive gas containing only C02 and N2 was used

for comparison of test sorbents and detailed kinetic studies

of the selected sorbents. The effect of the background gas

composition will be discussed once again in Chapter 7.

4.3 Comparison of Test Sorbents

Calcination results for the six calcium carbonate

precursors (sorbents 1 to 6) are compared in Figures 4.9 and

4.10. Sorbent 1 results are included in both figures for

reference purposes. Note that all sorbents were calcined at

the same conditions. As shown in the figures, all calcination

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80

Calcination: 750 C, 1 atm . N2 Hooting Rato: 50C /m in.

0 20 40 60 80 TIME. MIN.

Figure 4.9 Comparison of Calcination Kinetics; Sorbents 1, 2, 4, and 5

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81

Calcination: 750 C, 1 atm, N2 Hooting Rato: 50C /m in. Sorbont 1 (R -7 4 ) Sorbont 3 ( R - M ) Sorbont 6 (R -1 2 0 )

W V V W I W B—B-P-B 'OB

TIME, MIN.

Figure 4.10 Comparison of Calcination Kinetics; Sorbents 1, 3, and 6

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82

results were qualitatively similar. The calcination rate

became appreciable at about 625°C. Complete calcination,

corresponding to constant W/Wo values, occurred in the range

of 43 to 75 minutes. The difference in time for complete

calcination was attributed primarily to particle size

effects. Differences in W/Wo at complete calcination were due

to differences in purity. While the final weight of sorbent

1 (pure CaC03) was quite close to the theoretical value of

0.56, the final values for other sorbents were in the range

from 0.56 to 0.64.

Carbonation results of the six sorbents are shown in

Figures 4.11 and 4.12. Data for sorbent 1 are again included

in both figures for reference. Note that the carbonation

reaction for tests shown in Figure 4.11 was stopped after 2%

minutes, while the reaction was allowed to proceed for 20

minutes for the Figure 4.12 tests. Longer time was needed at

at 750°C (Figure 4.12) since the equilibrium C02 pressure

approached to actual C02 pressure. Differences in the initial

values of W/Wo were due to differences in final calcination

results. Each carbonation curve is similar. The final values

of W/Wo ranged from 0.82 to 0.85 at 630°C (Figure 4.11) while

the final W/Wo values at 750°C tests (Figure 4.12) were all

approximately 0.89.

The carbonation results for marl (sorbent 2) and chalk

(sorbents 3,4, and 6) sorbent precursors were unexpected.

Hartman et a l . (1978) reported that the reactivity of chalks

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14* CoWnafon: 750 C, M2,1 atm Carbonoffen: C30C, 5 .6 Z C 0 2 /N 2 ,1

0.90

-e-Sorbent 1(0-74) Sorbent 4 (8 -8 2 )

Sorbent 2 (R -8 4 )

Sorbent 5(R~85)

«0 120 100 TIME, SEC.

Figure 4.11 Comparison of Carbonation Kinetics; Sorbents 1, 2, 4, and 5

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84

Calcination: 750 C, N 2 ,1 atm Carbonation: 750 C. 5 .6 Z C 0 2 /N 2 ,1 atm 1.00-

•e-Sorbont 1(R-102)

1 3 5 7 9 11 15 15 17 19 TIME, MN.

Figure 4.12 Comparison of Carbonation Kinetics; Sorbents 1/ 3, and 6

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and marls was significantly greater than the reactivity of

limestone in their sulfation studies. The reactivity

increases were attributed to the greater porosity of CaO

formed from chalks and marls. However, as seen in the

figures, the carbonation behavior of all sorbents was similar

to that of the reagent grade CaC03.

An alternate approach to increasing sorbent reactivity

was tested by the use of sorbents 7, 8, and 9. Sorbents 7 and

8, consisting of reagent grades of calcium acetate and

calcium sulfate, respectively, were selected based upon the

logic that decomposition of the precursor would involve

driving off a significantly increased quantity of volatile

material leaving CaO sorbent with increased pore volume and,

presumably, greater carbonation reactivity.

Figure 4.13 shows calcination and carbonation results

for one complete cycle of sorbent 7. Although the high

pressure electrobalance was used, both calcination and

carbonation were at one atmosphere. The precursor,

Ca(C2H302)2.xH20 containing 8.3% H20, was heated in N2 as shown.

Water of hydration was driven off in two increments in the

temperature range 100-300°C, leaving Ca(C2H302) 2 with W/Wo a

0.92. Acetate decomposition began at about 370°C and a

constant weight plateau was reached at 500°C with W/Wo a

0.58, corresponding to CaC03 formed from the original

hydrated calcium acetate. Additional weight loss to W/Wo =

0.325 occurred in the vicinity of 750°C. No further weight

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Sorbent 7 (HP067) 1.00 Calcination: N 2 ,1 atm - 1,000 Carbonation: 750C, 1 5Z C 02 /N 2 ,1 atn.

-800

-6 0 0 CaC03

-400 C TEMPERATURE.

-200

0 SO 100 150 200 250 TIME, MIN.

Figure 4.13 Decomposition and Carbonation Kinetics; Sorbent 7

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loss occurred during 60 minutes in N2 at 750°C, and the final

weight corresponded to the theoretical value for the

production of CaO from calcium acetate containing 8.3% H20.

When carbonation was initiated after 210 minutes, the weight

gain was rapid and the final value of W/Wo = 0.57

corresponded closely to the value expected for total

conversion of CaO to CaC03 (W/Wo = 0.58).

Decomposition of hydrated calcium sulfate, CaS04.2H20

(sorbent 8), is illustrated in Figure 4.14. The atmosphere

during CaS04 decomposition was 50% N2 - 50% H2, with the

hydrogen added to promote the removal of sulfur as H2S. H20

was driven-off at about 300°C. CaS04 began to decompose after

approximately 80 minutes at about 900°C. Instead of forming

CaO, the final decomposition product was CaS. After 13 0

minutes, the carbonation gas was introduced, and CaS, as

shown in the figure, had no carbonation activity. Hydrated

calcium sulfate, therefore, could not be considered as a

sorbent precursor.

Sorbent 9 was a commercial dolomite containing

approximately equal molar quantities of CaC03 and MgC03

obtained from National Lime Co. (see Table 3-5). Dolomite was

chosen to test the effect of magnesium on the reactions.

Calcination of both CaC03 and MgC03 should contribute to

increased porosity in the mixed oxide product. At the

carbonation conditions of interest, MgO will not react with

C02 so that the pores created by MgC03 calcination should

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1,000

1.00

CoS04

«s 500 IO 0.60 in TEMPERATURE, TEMPERATURE, C

CoS

CaO ! Sorbent 8 (R-140)

0 40 80 120 160 TIME, MIN.

Figure 4.14 Decomposition of Calcium Sulfate; Sorbent 8

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remain open and prevent the pore closure experienced by pure

CaC03. Figure 4.15 shows the results for one complete

calcination-carbonation cycle of sorbent 9. Calcination began

at approximately 450°C and was complete at about the time the

sample reached the desired final temperature of 750°C.

Calcination of MgC03 should occur at lower temperature,

followed by calcination of CaC03. However, no clearcut

distinction in the weight loss curve associated with MgC03

and CaC03 decomposition was observed. The final value of W/Wo

= 0.525 corresponded closely to the loss on ignition value

reported by National Lime, and represented complete

conversion of CaC03 and MgC03 to CaO and MgO.

Carbonation was carried out in 15% C02/N2 at 750°C and 1

atm. Carbonation behavior was qualitatively similar to that

exhibited by other sorbents. A rapid initial reaction period

lasting less than 5 minutes was followed by an abrupt

transition to a slow reaction phase. The transition, however,

occurred at W/Wo « 0.73, which corresponds to a fractional

calcium carbonation of 0.85, significantly higher than that

observed using pure CaC03. After one hour of carbonation

reaction, the W/Wo value was 0.75, which corresponds to 0.93

fractional carbonation of calcium.

From the above test results, three sorbents were chosen

to be studied in a greater detail. Sorbent 1 served as the

standard sorbent. Sorbent 7 was selected due to the high

porosity created during calcination which caused high

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1,000 Sorbent 9 (HP057) Calcination: N 2,1 atm Carbonation: 15X C 02/N 2,1 atm

CaC03 + MgO

/ C TEMPERATURE,

150 200 TIME, MIN.

Figure 4.15 Calcination and Carbonation Kinetics; Sorbent 9

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. carbonation reactivity. Sorbent 9 was chosen because

decomposition of MgC03 to MgO helps create "extra" pore

volume during calcination, hence increasing the carbonation

reactivity. In addition, related studies by Narcida (1992)

showed that the three sorbents produced a wide variation of

structural property changes during their calcination and

carbonation reactions, as discussed in Chapter 2.

Figure 4.16 provides a direct comparison of first-cycle

carbonation behavior of the three sorbents at the same

carbonation conditions. While each sorbent exhibits

qualitatively similar behavior, it is clear that sorbents 7

and 9 can achieve greater than 90% carbonation compared to

only 80% carbonation for sorbent 1.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92

1.00 Swbmt 9 (HP057)

Sorbmt 7 (HP067) x 0 .8 0 *** |, |„r—mi* ^ ^ Sorbent 1 (HP066)

0.20 Calcfnotion: 750C, N 2,1 atm Carbonation: 750C, 15XC02/N2,1 atm

0 10 20 30 40 50 7060 TIME, MIN.

Figure 4.16 Comparison of First-Cycle Carbonation Kinetics; Sorbents 1, 7, and 9

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 5

Experimental Results:

Two-Cycle Reaction Studies

This chapter focuses on studies of two-cycle

calcination-carbonation kinetics of the three base sorbents,

selected in the previous chapter, as a function of

temperature, pressure, and C02 gas composition. Table 5-1

shows the reaction parameters tested in this study.

Calcination pressure was one atmosphere and the calcination

gas was pure nitrogen. As discussed later in Chapter 6,

calcination pressure does not significantly affect the

carbonation performance. As a result of Table 5-1, the

complete matrix consists of 243 tests. However, due to

reaction equilibrium considerations and on the basis of

results from the earlier tests, only 98 tests were actually

carried out. In addition to determining the effect of

reaction parameters, the two-cycle tests provided preliminary

information on sorbent durability which is a primary concern

of commercial use.

The complete test matrix is shown in Tables 5-2, 5-3,

and 5-4 for sorbents 1, 7, and 9, respectively. The 98 runs

which were completed are designated in these tables by run

number. Duplicate runs were made periodically as indicated to

check reaction reproducibility.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94

Table 5-1

Two-Cycle Reaction Parameters

Parameter No. of Parameter Conditions Levels

Calcination Temperature 750, 825, and 900°C

Carbonation Temperature 550, 650, and 750°C

Carbonation Pressure 3 1, 5, and 15 atm

C02 Mol Fraction 3 0.01, 0.05, and 0.15

Base Sorbent 3 Sorbent 1, Sorbent 7, and Sorbent 9

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Table 5-2 Matrix of Two-Cycle Runs for Sorbent 1

Calcin. Carbon. Carbon. Carbonation Pressure Temp. Temp. co2 (°C) (°C) (% Vol) 1 atm 5 atm 15 atm

900 750 15 HP048 HP082 HP040 900 750 5 * * * ★ * ★ * * *

900 750 1 * * * * * * * it * 900 650 15 HP084 HP096 * * *

900 650 5 ★ * it *** ★ ★ *

900 650 1 *** *** * * * 900 550 15 HP083 HP099 *** 900 550 5 HP085 *** *** 900 550 1 HP086 ******

825 750 15 HP047 HP113 HP039

825 750 5 *** *** ***

825 750 1 * * * * "k * *** 825 650 15 HP045 HP117 HP134 825 650 5 HP051 *** * * *

825 650 1 * * ★ *** *** 825 550 15 HP125 HP120 ***

825 550 5 HP129 ★ ★ Hr *** 825 550 1 HP126 *** ***

750 750 15 HP066 HP063 HP032 HP095

750 750 5 * * * *** HP034 750 750 1 * * * *** HP033 750 650 15 HP046 HP097 HP141

750 650 5 HP043 * * * ***

750 650 1 * * * *** HP133 HP137

750 550 15 HP049 HP098 HP139

750 550 5 HP130 *** ***

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Table 5-3 Matrix of Two-Cycle Runs for Sorbent 7

Calcin. Carbon. Carbon. Carbonation Pressure Temp. Temp. C02 (°C) (°C) (% Vol) 1 atm 5 atm 15 atm

900 750 15 HP055 ★ * * HP076 900 750 5 ★ * * HP109 * * * 900 750 1 *** *** * * * 900 650 15 *** *** HP091 900 650 5 * * * * * ★ *** 900 650 1 *** * ★ ★ *** 900 550 15 * * * ★ * * HP100 900 550 5 * * * *** *k* 900 550 1 *** •k-kic "kieit

825 750 15 HP053 *** HP106 825 750 5 *** HP108 * * *

825 750 1 *** * * * itiek 825 650 15 HP054 *** HP121

825 650 5 HP052 HP118 • kick

825 650 1 *** * ** i tiek 825 550 15 HP123 ★ ★ ★ HP127

825 550 5 *** HP131 k k k

825 550 1 *** •k it it k k k

750 750 15 HP067 HP064 HP036 HP068

750 750 5 *** HP124 HP037

750 750 1 *** *** HP038

750 650 15 HP056 HP110 HP101

750 650 5 *** * * * *** 750 650 1 *** HP147 *** 750 550 15 HP061 HP144 HP128

750 550 5 HP093 * * * * * *

750 550 1 HP060 HP145 •kic it

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Table 5-4 Matrix of Two-Cycle Runs for Sorbent 9

Calcin. Carbon. Carbon. Carbonation Pressure Temp. Temp. C02 (°C) (°C) (% Vol) 1 atm 5 atm 15 atm

900 750 15 HP062 *** HP077 900 750 5 *** ★ ★ ★ HP088 900 750 1 *** * ★ * HP087 900 650 15 * * * *** *** 900 650 5 *** *** ★ ★ *

900 650 1 ★ * ★ *** HP090 900 550 15 * * ★ *** *** 900 550 5 * ★ ★ ★ * * *** 900 550 1 *** * ** HP089

825 750 15 HP078 HP112 HP103 825 750 5 *** * * * ***

825 750 1 * * * *** HP135 825 650 15 * ★ * ★ ★ * HP115 825 650 5 *** *** HP132

825 650 1 * * * it it it HP116

825 550 15 *** it it it ***

825 550 5 * * ★ it it it ***

825 550 1 ★ * * ititit HP122

750 750 15 HP057 HP069 HP075 HP105

750 750 5 *** ititit HP092

750 750 1 ititit *** HP080

750 650 15 HP071 HP111 HP136

750 650 5 HP072 * * * *** 750 650 1 *** ★ * * HP102 750 550 15 HP073 HP143 HP140 750 550 5 HP074 *** HP142 750 550 1 HP094 *** HP114

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98

The electrobalance response through two complete cycles

for duplicate tests using sorbent 9 (HP057 and HP105) is

shown in Figure 5.1. Both samples were calcined at 750°C and

1 atm N2. Carbonation was carried out in 15% C02/N2 at 750°C

and 1 atm. Calcination of the dolomite precursor consisting

of 54.5% CaC03 and 45% MgC03 (mass %) produced the final value

of W/Wo = 0.528 which corresponds to complete calcination of

CaC03 and MgC03 to CaO and MgO. Complete calcination was

achieved in both cycles of both tests. Carbonation gas

consisting of 15% C02 in N2 was introduced after 210 minutes.

Carbonation was quite rapid initially but after 5 minutes the

rate decreased abruptly and was quite slow thereafter. After

carbonation for 40 minutes, fractional carbonation for the

two cycles of the two tests varied from 0.90 to 0.93. As seen

in the figure, the reproducibility was quite good, and is

typical of all cases in which repeat tests were carried out.

5.1 Reactivity and Capacity Indices

Because of the large amount of experimental data

acquired in each run, it was necessary to develop a means of

reducing the data to a more manageable form to permit direct

comparison of results and to evaluate the effect of the

reaction parameters. Therefore, indices based upon fractional

carbonation at equivalent reaction times in both the early

rapid reaction phase and the final slow reaction phase were

developed to provide this comparison basis. Selection of the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sorbent 9 Calcination: 750C, N 2 ,1 atm I.OOh b Carbonation: 750C, 152C02/N 2,1 atn

a HP057 o HP105 i ft se 6 o ft 0.80- ft

ft o to nr ! i 0.60-

I T 0 too 200 300 400 TIME, MIN.

Figure 5.1 Reaction Reproducibility of Two Calcination Carbonation Cycles for Sorbent 9

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100

appropriate reaction time for the slow phase represented no

major problem since the slope of the weight-time curve for

each run approached zero during the latter stages. Selection

of the proper time for comparing results in the rapid

reaction phase, however, was complicated by two factors. The

first was associated with a time lag between opening the

reactive gas valve in the reactor sidearm and the sample

being exposed to the full reactive gas concentration. The

second factor was the large slope of the weight-time curve

early in the reaction. A relatively small time error would

result in a large error in the index.

This problem was solved by evaluating the lag time, t0,

associated with each run as described below. Figure 5.2 shows

the general response of the weight-time curve during a

carbonation cycle. Low C02 mol fraction at high pressure was

chosen to accentuate the time lag. t = 0 corresponds to

opening the sidearm reactive gas valve. There was no reaction

for approximately 5 minutes thereafter. In next couple of

minutes the reaction rate gradually increased and after about

7 minutes there was a period in which the weight-time curve

was essentially linear. During the first 5 minutes the

sorbent was exposed to essentially no C02; between 5 and 7

minutes the C02 concentration increased from zero to its

steady-state value (1% vol). The duration of the unsteady

state period was found to a strong function of pressure and

a weak function of temperature and C02 mol fraction. The lag

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 101

Sorbont 9 (HP080) Coletnotion: 7S0C, N 2 ,1 atm Carbonation: 750C, 1 IC 0 2 /N 2 ,15 atm

i t-to=1 mln.

TIME, MIN.

Figure 5.2 Determination of the Time Lag, t0, during Carbonation Reaction

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102

time t0 shown in Figure 5.2 was obtained by extrapolating the

linear portion of the weight-time curve to the initial

weight. Constant values of (t-tQ) , therefore, were taken to

represent equivalent reaction time. Table 5-5 summarizes the

tc values for the first and second cycles for each set of

reaction conditions. No dependence of t0 on either

calcination temperature or sorbent precursor was found except

for carbonation at 750°C, 1 atm, and 15% C02, reaction

conditions which were quite close to the equilibrium

conditions for carbonation. Therefore, multiple table entries

are included for these conditions. In other cases there are

two t0 values for each set of reaction conditions. These

represent cycles 1 and 2, respectively. There is either no

change or a slight increase in t0 in the second cycle. The

overall values range from 6.9 minutes at high temperature,

high pressure, and low C02 mol fraction to 0.2 minutes at low

temperature, low pressure, and high C02 mol fraction. Each

entry represents the average value from all runs at the

particular set of conditions.

Values of fractional carbonation at fixed values of (t-

t0) were used to compare the kinetics of different runs. As

a result of trial-and-error comparison, (t—t0) = 1 minute was

chosen as the most suitable time for comparing kinetics

during the initial reaction phase, while (t-t0) = 40 minutes

was chosen to compare the slow reaction phase. In Figure 5.2,

for example, the rapid phase lasts for several minutes and

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Table 5-5

Summary of the Lag Time, t0, at Various Reaction Conditions

Carbonation t0 (min ) Temperature Carbonation Pressure (°C) % C02 1 atm 5 atm 15 atm

750 15 0.6/* (S-l) 0.9/1.0 0.9/1.0 1.4/* (S-7) 0.3/’ (S-9)

750 5 *** 2.2/2.2 2.2/2.2

750 1 *** *** 6.8/6.9

650 15 0.2/0.3 0.7/0.8 1.2/1.3

650 5 0.3/0.4 0.9/1.0 1.5/1.5

650 1 *** 2.0/2.5 2.7/3.0

550 15 0.2/0.3 0.7/0.7 1.1/1.1

550 5 0.3/0.3 0.7/0.7 1.5/1.3

550 1 0.2/0.3 1.3/1.3 2.0/2.1

Calcination t0 (min ) Temperature (°C) S-l S-7 S-9

900 1.4 1.7 1.3 825 1.3 1.1 0.5 750 0.7 0.9 1.0 750 0.8 0.9 0.5

^ no tests were made at these conditions due to reaction equilibrium considerations

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104

values of (t-t0) > 1 minute could be used. However, at high

C02 concentration and low pressure, the rapid reaction phase

terminates much sooner and values of fractional carbonation

at (t-t0) > 1 minute would be inappropriate. The choice of

(t-t0) = 40 minutes to compare the slow reaction phase is

arbitrary. It is obvious from Figure 5.2 that the rate of

increase in fractional carbonation is quite slow in the

vicinity of 40 minutes, and approximately the same fractional

carbonation values would be obtained over a range of times.

In the following discussion, the terms reactivity,

reactivity maintenance, capacity, and capacity maintenance

are used. These are defined as follows:

Reactivity, R: - fractional carbonation after (t-t0) =

1 minute in cycle i.

Capacity, C; - fractional carbonation after (t-t0) =

40 minutes in cycle i.

Reactivity Maintenance, R,j - ratio of reactivity in

cycle j to reactivity in cycle 1.

Capacity Maintenance, C,j - ratio of capacity in cycle

j to capacity in cycle 1.

Experimental reactivity results for the two-cycle test

series are summarized in Tables 5-6, 5-7, and 5-8 for

sorbents 1, 7, and 9, respectively. Note that the arrangement

in these tables corresponds to the test matrix in Tables 5-2,

5-3, and 5-4. The two entries in each position correspond to

cycles 1 and 2, respectively. For example, in the first

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Table 5-6 Matrix of First and Second Cycle Reactivity for Sorbent 1 ' ' ■'. Calcin. Carbon. Carbon. Carbonation Pressure Temp. Temp. C02 <°C) (°C) (% Vol) 1 atm 5 atm 15 atm

900 750 15 .21/.11 .56/.47 .37/.32 900 750 5 * * * *** * * * 900 750 1 it it it * * * *** 900 650 15 .65/.41 .59/.40 * * * 900 650 5 * ★ * *** * * * 900 650 1 *** *** * * * 900 550 15 .56/.14 .55/.16 kkk 900 550 5 .43/.19 ★ * * kkk 900 550 1 .16/.06 ■kitit kkk

825 750 15 .22/.14 .56/.56 .39/.37 825 750 5 * ★ * kkit kkk 825 750 1 *** kkk kkk

825 650 15 .68/.50 .52/.43 .38/.37 825 650 5 .30/.17 * ★ ★ kkk 825 650 1 * * * * * * kkk

825 550 15 .60/.41 .51/.36 kkk 825 550 5 .45/.24 •kkk kkk 825 550 1 .11/.08 kkk kkk

750 750 15 .23/.22 .51/.52 .37/.39 .20/.18 750 750 5 it it it * * * .21/.21 750 750 1 kkk kkk .10/.09 750 650 15 .67/.55 .63/.53 .42/.43 750 650 5 .25/.27 *** ***

750 650 1 ★ * * kkk .15/.10 .10/.11 750 550 15 .63/.49 .57/.43 .41/.33 750 550 5 .47/.40 *** * * * 750 550 1 .05/.04 *** * * *

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Table 5-7 Matrix of First and Cycle Reactivity for Sorbent 7

Calcin. Carbon. Carbon. Carbonation Pressure Temp. Temp. C02 (°C) (% Vol) (°C) 1 atm 5 atm 15 atm

900 750 15 .13/.08 *** .59/.48 900 750 5 *** -30/.29 kkk 900 750 1 * * * * * * kkk 900 650 15 * * * ★ * * .61/.41 900 650 5 * * ★ *** * * ★ 900 650 1 *** kkk kkk 900 550 15 ★ ★ * * * ★ .47/.18 900 550 5 *** *** ★ * * 900 550 1 *** *** kkk

825 750 15 .13/.27 kkk •.51/.57 825 750 5 ★ ★ * .24/.25 kkk 825 750 1 * * ★ *** kkk 825 650 15 .76/.40 * ** .47/.51 825 650 5 .42/.20 .43/.33 kkk 825 650 1 *** ■kitit kkk 825 550 15 .54/.43 kkk .44/.35

825 550 5 * * ★ .48/.24 *** 825 550 1 •Mick *** ***

750 750 15 .13/.29 .72/.72 .55/.60 .08/.28 750 750 5 *** .25/.27 .32/.27 750 750 1 *** *** .07/.10 750 650 15 .75/.68 .79/.73 .55/.58

750 650 5 *** *** kkk 750 650 1 *** .10/.11 kkk 750 550 15 .62/.57 .58/.53 .48/.42 750 550 5 .54/.47 *** kkk 750 550 1 .08/.07 .11/.11 kkk

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Table 5-8 Matrix of First and Second Cycle Reactivity for Sorbent 9

Calcin. Carbon. Carbon. Carbonation Pressure Temp. Temp. co2 (°C) (°C) (% Vol) 1 atm 5 atm 15 atm

900 750 15 .15/.13 *** .53/.44

900 750 5 *** * k k .28/.23

900 750 1 * * * ir k k .05/.00 900 650 15 * * * *** ***

900 650 5 * * * it it it ***

900 650 1 * * * • k ick .12/.15

900 550 15 *** •kkk ***

900 550 5 *** k k k ★ * *

900 550 1 * * ★ kkk .11/.12

825 750 15 .20/.14 .73/.61 .38/.36

825 750 5 *** k k k ***

825 750 1 ★ ** k k k .08/.07

825 650 15 *** k k k .50/.42

825 650 5 *** k k k .28/.26

825 650 1 *** k k k .07/.11

825 550 15 * * * k kk ★ * *

825 550 5 *** kk k k kk

825 550 1 ★ ★ * k kk .09/.11

750 750 15 .23/.19 .69/.71 .51/.48 .17/.15

750 750 5 * * * k k k .32/.25

750 750 1 k kk kk k .16/.05 750 650 15 .80/.68 .72/.66 .49/.54 750 650 5 .34/.33 * * * *** 750 650 1 *** *** .11/.08 750 550 15 .73/.49 .70/.44 .41/.33

750 550 5 .49/.40 k kk .27/.19

750 550 1 .11/.10 k k k .13/.11

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matrix position of Table 5-6 the value of reactivity for

cycle 1 is 0.21 while that for cycle 2 is 0.11. The

reactivity maintenance in this case is R12 = 0.11/0.21 = 0.52,

indicating a rather severe decrease at these reaction

conditions. Increased second-cycle reactivity was observed in

a number of instances. For example, from Table 5-7 using

sorbent 7 at 750°C calcination and carbonation temperatures,

15 atm carbonation pressure, and 0.15 mol fraction C02 in the

carbonation gas, the sorbent reactivity increased from R, =

0.55 to R2 = 0.60, yielding R12 = 1.09.

Tables 5-9, 5-10, and 5-11 summarize the comparable

results for sorbent capacity. The two entries in each matrix

position represent results from cycles 1 and 2. For example,

the first entry for sorbent 1 (Table 5-9) shows Cj = 0.77 and

C2 = 0.57 to give the capacity maintenance (C12) of 0.74. The

capacity results in the tables show, for most test

conditions, small to quite significant capacity loss in the

second cycle (C12 < 1.0). In a few cases, however, a slight

increase in capacity was observed. For example, for sorbent

9 (Table 5-11) at a calcination temperature of 750°C, and

carbonation conditions of 650°C, 5 atm, and 15% C02, C, = 0.93

and C2 = 0.94 yielding C12 = 1.01. Since the maximum value of

Cj = 1.0, there is little opportunity for an increase in the

capacity maintenance index when complete carbonation is

closely approached.

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Table 5-9 Matrix of First and Second Cycle Capacity for Sorbent 1

Calcin. Carbon. Carbon. Carbonation Pressure Temp. Temp. C02 (°C) (°C) (% Vol) 1 atm 5 atm 15 atm

900 750 15 .77/.57 .76/.58 .77/.62 900 750 5 ★ * ★ * * * *** 900 750 1 * * * *** kkk 900 650 15 .70/.46 .71/.49 kkk 900 650 5 ■k k * * * * kkk 900 650 1 ★ ★ * kkk kkk 900 550 15 .60/.35 .60/.37 kkk 900 550 5 .63/.41 kkk kkk 900 550 1 .62/.45 kkk kkk

825 750 15 .78/.60 .76/.66 .78/.64 825 750 5 *** *** kkk 825 750 1 * ★ * kkk kkk 825 650 15 .74/.56 .67/.49 .64/.48 825 650 5 .74/.54 kkk kkk 825 650 1 * * ★ kkk kkk

825 550 15 .63/.44 .58/.39 kkk 825 550 5 .62/.41 ★ ★ ★ kkk 825 550 1 .65/.48 kkk kkk

750 750 15 .79/.68 .81/.70 .77/.66 .78/.67 750 750 5 *** * * * .77/.67 750 750 1 kkk kkk .77/.65 750 650 15 .73/.59 .71/.57 .67/.54

750 650 5 .76/.60 kkk * * ★ 750 650 1 *** kkk .75/.60 .71/.58 750 550 15 .67/.52 .62/.48 .60/.43 750 550 5 .63/.47 *** kkk 750 550 1 .72/.52 *** .62/.48

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Table 5-10 Matrix of First and Second Cycle Capacity for Sorbent 7

Calcin. Carbon. Carbon. Carbonation Pressure Temp. Temp. C02 <°C) (°C) (% Vol) 1 atm 5 atm 15 atm

900 750 15 .94/.81 kkk .96/.94 900 750 5 *** .86/.89 kkk 900 750 1 *** * * * kkk 900 650 15 *** *** .94/.76 900 650 5 *** *** kkk 900 650 1 * it k *** kkk 900 550 15 kkk *** .93/.46 900 550 5 kkk *** * * * 900 550 1 ★ * * *** * * ★

825 750 15 .94/.87 kkk .98/.95 825 750 5 * * k .91/.97 *** 825 750 1 kkk *** * * *

825 650 15 .92/.72 *** .93/.88 825 650 5 .89/.86 .95/.94 kkk 825 650 1 * * * kkk kkk

825 550 15 .91/.54 kkk .94/.51 825 550 5 *** .93/.59 *** 825 550 1 * * * ★ * * ★ ★ ★

750 750 15 .95/.94 1.0/.95 .98/.94 .95/.93

750 750 5 *** .97/.92 .97/.94 750 750 1 ■kitit kkk .93/.90 750 650 15 .92/.91 .92/.93 .95/.95 750 650 5 *** *** *** 750 650 1 *** .92/.90 ***

750 550 15 .92/.75 .94/.73 .94/.73 750 550 5 .94/.76 *** *** 750 550 1 .88/.67 .90/.69 ** *

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Table 5-11 Matrix of First and Second Cycle Capacity for Sorbent 9

Calcin. Carbon. Carbon. Carbonation Pressure Temp. Temp. C02 (°C) (°C) (% Vol) 1 atm 5 atm 15 atm

900 750 15 .92/.84 ★ ★ * .92/.89 900 750 5 *** kkk .93/.89 900 750 1 * * * kkk .90/.84 900 650 15 "kick kkk kkk 900 650 5 kkk kkk *** 900 650 1 kkk kkk .87/.84 900 550 15 kkk kkk kkk 900 550 5 kkk *** kkk 900 550 1 kkk *** .84/.68

825 750 15 .94/.90 .92/.94 .94/.93 825 750 5 kkk *** kkk 825 750 1 kkk *** .97/.92 825 650 15 kkk *** .94/.91 825 650 5 kkk *** .93/.87 825 650 1 kkk * * * .95/.91 825 550 15 *** kkk *** 825 550 5 kkk *** kkk 825 550 1 kkk kkk .90/.73

750 750 15 .93/.91 .98/.97 .96/.96 .92/.90

750 750 5 kkk *** .96/.95 750 750 1 kkk * * * .93/.90 750 650 15 .95/.96 .93/.94 .96/.93 750 650 5 .94/.94 * * * *** 750 650 1 *** kkk .95/.93 750 550 15 .91/.78 .93/.79 .90/.78 750 550 5 .90/.75 * * * .92/.61

750 550 1 .86/.69 *** .90/.74

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These index values permit the effect of individual

reaction parameters to be evaluated and allow direct

comparison of the performance of the three sorbents under

equivalent reaction conditions. These evaluations are

discussed in the following sections.

5.2 Reaction Parameter Evaluation

5.2.1 The Effect of Calcination Temperature

Reactivity and capacity results suggest that the lowest

calcination temperature, 750°C, should be used. Higher

calcination temperature, in particular 900°C, has an adverse

effect on both reactivity and capacity. Figures 5.3, 5.4,

5.5, and 5.6 illustrate the effect of calcination temperature

on reactivity and capacity performance. All runs in these

figures were carried out at the same carbonation conditions.

Of the twelve curves represented in Figures 5.3 and 5.4,

eleven exhibit a negative slope. Only the first-cycle

reactivity of sorbent 7 (Figure 5.3) shows slightly improved

performance following high calcination temperature. The

magnitudes of the negative slopes are greater in the second

cycle (Figure 5.4) suggesting that the adverse effect of high

calcination temperature increases with increased number of

cycles. These second cycle results are emphasized in Figures

5.5 and 5.6 where two-cycle reactivity maintenance and

capacity maintenance are plotted against calcination

temperature.

FIRST CYCLE REACTIVITY, R1, AND CAPACITY, C1 0.80 1.00 700 Reactivity and Capacity and Reactivity abnto: 5C 5C2/ 1 atm ,1 2 N 15XC02 / 750C, Carbonation: acnto: 1 atm ,1 2 N Calcination: S-1 ♦ 750 ACNTO TEMP. C ., P M E T CALCINATION 7 - S * 800 - A • -9 S

850 900 950 113

SECOND CYCLE REACTIVITY, R2. AND CAPACITY. C 2 0.60 0.80 0.00 0 70 0 80 0 950 900 850 800 750 700 Cycle Reactivity and Capacity and Reactivity Cycle C2 T ACNTO TM. C TEMP., CALCINATION abnto: 5C 5 2N21 atm 2,1 02/N C Carbonation: 750C, 15Z acnto: 1 atm ,1 2 Calcination: N T T T A- -9 -S •A

114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Figure 5.5 Effect of Calcination Temperature on Reactivity on Temperature Calcination of Effect 5.5 Figure

REACTIVITY MAINTENANCE, R 12 0 5 900 850 700 Maintenance -7 S 5 800 750 ACNTO TM. C TEMP., CALCINATION abnto: 5C1X0/21 atm 750C.15XC02/N2,1 Carbonation: atm ,1 2 N Calcination: S-1

-9 S 950 115

CAPACITY MAINTENANCE, C 1 2 0.60 0.80 1.00 700 Maintenance 750 abnto: 5C1X0/21 atm Carbonation: 750C.15XC02/N2.1 atm ,1 2 Calcination: N ACNTO TM. C TEMP., CALCINATION 800 850

900 S-1 -7 S -9 S 950

116 117

There are 19 sets of data at which a complete comparison

of the effect of the three calcination temperatures at

constant carbonation conditions is possible. The advantages

associated with low calcination temperature are most apparent

with respect to first-cycle capacity, Clf and capacity

maintenance, C12. In 15 of the 19 data sets, the lowest

calcination temperature resulted in the highest value for

these indices. Conversely, in 15 of the 19 cases the highest

calcination temperature resulted in the lowest indices

values.

5.2.2 The Effect of Carbonation Temperature

In evaluating the effect of carbonation temperature on

the reaction characteristics, the equilibrium C02 partial

pressure at the temperature of interest must be considered.

A number of tests were eliminated in the matrix (Tables 5-2,

5-3, and 5-4) due to the equilibrium restrictions. Even at

conditions where tests were carried out, one must be aware of

equilibrium when interpreting the results. At 750°C the

equilibrium C02 pressure is about 0.08 atm. At 1 atm total

pressure no reaction will occur when either 1% or 5% C02 is

included in the carbonation gas; the effective C02 pressure

in 15% C02 is reduced by about one-half. At 550°C, however,

the equilibrium C02 pressure is sufficiently small that even

data at 1 atm total pressure and 1% C02 is free from

equilibrium restrictions.

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Figure 5.7 illustrates the effect of carbonation

temperature on first cycle reactivity, R,. Note that the

large decrease in reactivity at 750°C is due to the

equilibrium C02 pressure, as mentioned above. At 550°C and

650°C the equilibrium C02 pressure is small compared to the

actual C02 pressure, and as shown in Figure 5.7, there is a

small increase in reactivity with temperature. Figure 5.8

shows a more realistic view of the effect of carbonation

temperature on reactivity. Note that the equilibrium C02

pressure is very small compared to the actual 2.25 atm C02

partial pressure. As shown in the figure, there is a small

increase in reactivity through the entire temperature range

for sorbents 7 and 9, but a small decrease in reactivity for

sorbent 1 between 650°C and 750°C. The overall lack of a

strong temperature dependence suggests that the reactivity is

influenced more by transport resistances than the surface

chemical reaction.

The most surprising effect of carbonation temperature

was an apparent sharp decrease in capacity maintenance, C12,

at the lowest carbonation temperature of 550°C. Table 5-12

summarizes the average and standard deviation values of

first-cycle capacity (C,) , second-cycle capacity (C2) , and

capacity maintenance (CI2) for all equivalent data sets from

Tables 5-9, 5-10, and 5-11. Each sorbent shows a significant

drop in capacity maintenance at 550°C compared to the higher

temperatures. A caution in interpreting the Table 5-12

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119

Calcination: 750C, N 2 ,1 atm Caitonatton: 15ZC02/N2,1 atm

oz 0.80

oc u

•A -S -9

0.00 T T 500 600 700 800 CARBONATION TEMP., C

Figure 5.7 Effect of Carbonation Temperature on First-Cycle Reactivity; Carbonation at 1 atm in 15% C02/N2

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120

0.80- Calcination: 750C, H 2 ,1 atm Carbonation: 15ZC02/N2,15atm

“ 0.60- m >

aci 0.40' ui _i o &) ___ £ 0.20<

S-1 S -7 S -9

0.00> 500 600 700 800 CARBONATION TEMP., C

Figure 5.8 Effect of Carbonation Temperature on First-Cycle Reactivity; Carbonation at 15 atm in 15% C02/N2

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 121

Table 5-12 The Average and Standard Deviation Values of First and Second Cycle Capacity and its Capacity Maintenance for Sorbents 1, 7, and 9

Carbonation No.of First-Cycle Second-Cycle Capacity Temperature Data Capacity Capacity Maintenance Sets C IS) ______CC.J______(C2) ______[Cl2) _

Sorbent 1 8

750 0.78±0.02 0.64±0.05 0.82 650 0.71±0.03 0.54±0.05 0.76 550 0.62±0.03 0.43±0.06 0.69

Sorbent 7 7

750 0.96±0.03 0.94±0.03 0.98 650 0.93±0.02 0.87±0.09 0.94 550 0.9310.03 0.6210.12 0.67

Sorbent 9 6

750 0.9510.03 0.9210.04 0.97 650 0.9410.03 0.9210.04 0.98 550 0.9010.03 0.7510.04 0.83

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 122

entries is necessary. The only valid comparison is of the

effect of carbonation temperature on an individual sorbent;

in this case the data sets are equivalent. It is not valid to

compare the performance of the three sorbents at a fixed

carbonation temperature since the data sets involved in such

a comparison would not be equivalent. A general trend to low

Cj2 values at the lowest carbonation temperature is shown in

Figure 5-9.

Other researchers have also reported unexpected results

at carbonation temperatures near 550°C. Bhatia and Perlmutter

(1983) reported a change in activation energy for product

layer diffusion at 515°C suggesting a change in the reaction

mechanism. Anderson (1969) also reported a similar change in

activation energy for C02 exchange with calcite grains at

550°C. Mess (1989) reported a unique result from carbonation

of nonporous CaO particles at 550°C. Based on SEM

micrographs, he observed that nonporous CaO particles

carbonated at 550°C had completely different product

structure than particles carbonated at higher temperature. He

observed that the surface of the particles contained many

small crystallites of approximately 1 /zm size which protruded

from the product layer. This caused much rougher particle

surfaces than those carbonated at 600°C or above. Unlike

carbonation results at higher temperature, grain boundaries

were not observed at 550°C carbonation temperature.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 500 600 700 800 CARBONATION TEMP., C

Figure 5.9 Effect of Carbonation Temperature on Average Capacity Maintenance

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Carbonation temperatures of 650 and 750°C for sorbents

7 and 9 show little difference in capacity and capacity

maintenance. As seen in Table 5-12, the average values of

capacity for both sorbents are 0.90 or above for both cycle

1 and cycle 2 at 650 and 750°C (except for second-cycle

capacity of sorbent 7 at 650°C). Sorbent 1, however, shows a

significant decrease of capacity (from C, = 0.78 to C2 = 0.64

at 750°C and from C, = 0.71 to C2 = 0.54 at 650°C) .

5.2.3 The Effect of Carbonation Pressure

Like carbonation temperature, the effect of pressure on

the carbonation equilibrium must be considered. The effect of

carbonation pressure on first-cycle reactivity, R,, is shown

in Figure 5.10. The calcination temperature was 750°C, and

the carbonation conditions were 550°C and 15 atm in 15% C02

where the equilibrium effects were negligible. The reactivity

decreases with increasing pressure for all three sorbents.

The fact that reactivity decreases with increasing

carbonation pressure is consistent with the previous

conclusion that transport resistances are important in

establishing reactivity. If surface rate was controlling, one

would expect an increase in reactivity with pressure since

C02 concentration is directly proportional to pressure. In

contrast, both mass transfer coefficient and effective

diffusivity decrease with increasing pressure so that

transport resistances would produce the observed effect.

FIRST CYCLE REACTIVITY, R1 0.80 0.20 0 acnto: 5C N2, atm ,1 2 N 750C, Calcination: Reactivity abnto: 5C 152C02/N2 550C, Carbonation: 15 5 7 - S * PRESSURE, ATM 10

20 125

126

Reaction pressure has little effect on sorbent capacity in

either cycle, or on capacity maintenance. The capacity

maintenance behavior is illustrated in Figure 5.11. The

calcination temperature was 750°C, and the carbonation was in

15% C02 at 650°C. The curves are approximately horizontal for

each of the three sorbents with values of C12 in the range of

0.97 to 1.01 for sorbents 7 and 9 compared to about 0.81 for

sorbent 1. Eleven out of 13 equivalent data sets available

for this direct comparison show essentially no effect of

operating pressure on capacity maintenance.

5.2.4 The Effect of C02 Mol Fraction

Figure 5.12 illustrates the effect of C02 mol fraction

on first-cycle reactivity, R,. Calcination was carried out at

750°C, and carbonation was at 750°C and 15 atm. As expected,

the reactivity increases with increasing C02 mol fraction.

The absence of a linear dependence throughout the entire mol

fraction range is also reasonable. At the lowest C02 mol

fraction, the values of R! are in the range of 0.07 to 0.15;

an increase in Rj by a factor of 15 is impossible. In other

words, reactivity is not a diferential but an integral

function.

Sorbent capacity, on the other hand, is essentially

independent of C02 mol fraction as illustrated in Figure

5.13. Note that the reaction conditions are the same as in

Figure 5.12. The data for all three sorbents are almost

CAPACITY MAINTENANCE, C12 0.80 0.60 1.00 0 acnto:70, 1 atm ,1 2 N 750C, Calcination: abnHn 60, 15XC02/N2 CarbonaHon: 650C, Maintenance 5 PRESSURE, ATM 10

15 -7 S -9 S S-1 20

127 128

0.60 S -7 S -9

0.40 S -1

o a “ 0.20

Calcination: 750C, N 2 ,1 atm Carbonatton: 750C, 15 atm

0.00 .00 .10 C 02 MOLE FRACTION

Figure 5.12 Effect of C02 Mol Fraction on First-Cycle Reactivity

FIRST CYCLE CAPACITY, C l 1.00 ,00 abnfo: 5C 1 atm 15 750C, atm ,1 2 Carbonafion: N 750C, Calcination: Capacity 0 ML FRACTION MOLE C02 10

-7 S A ■ -9 S

129 130

horizontal, with slightly lower values of C, for sorbents 7

and 9 at 0.01 mol fraction due to the slow progress of the

reaction at low concentration and high pressure. In other

words, at these conditions the reaction was so slow that the

40 minute reaction time was not sufficient to establish

sorbent capacity.

5.3 Direct Comparison of Base Sorbents

There are 18 sets of reaction conditions at which all

three sorbents were tested. Four of the 18 data sets were

excluded in reactivity comparisons because the reaction

conditions were quite close to the equilibrium conditions.

However, these data were included in capacity and capacity

maintenance comparisons since C02 mol fraction has little

effect on capacity.

Sorbents 7 and 9 have a clear advantage over sorbent 1

in terms of both capacity and capacity maintenance. All 18

direct comparisons show that both sorbents 7 and 9 have

first-cycle capacities of 0.90 or above. For sorbent 1, on

the other hand, the first-cycle capacity ranges from 0.60 to

0.81. Moreover, sorbents 7 and 9 have better capacity

maintenance than sorbent 1. The C12 values of sorbent 1 range

from 0.72 to 0.86 while sorbents 7 and 9 have CI2 values from

0.76 to 1.01 and from 0.80 to 1.01, respectively.

Since first-cycle carbonation for sorbents 7 and 9 is

almost complete (conversion of 0.90 or above), it is

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difficult to make direct comparisons between the two

sorbents. However, sorbent 9 exhibits slightly higher values

of capacity maintenance. Of 18 data sets available for direct

comparison, 13 data sets confirm that sorbent 9 has a slight

advantage in term of capacity maintenance.

Capacity results for sorbent 9 can be somewhat

misleading. Capacity is a measure of fractional calcium

utilization, which provides an unambiguous basis for

comparison of sorbents 1 and 7, since both are essentially

pure CaO at the beginning of the carbonation cycle. Sorbent

9, however, at the beginning of carbonation contains more

than 40% (wt) inerts, primarily MgO. Therefore, on the basis

of unit mass of total sorbent, the C02 capacity of sorbent 9

is much less than that of either sorbent 1 or sorbent 7. This

subject will be discussed in more detail in Chapter 7.

In order to compare the reactivity of the three sorbents

it is necessary to exclude four of the 18 equivalent data

sets due to equilibrium considerations. Thirteen out of the

remaining 14 data sets show that sorbent 7 and sorbent 9

exhibit a higher reactivity in both cycles 1 and 2 than

sorbent 1. This behavior is attributed to the differences in

structural properties of each sorbent discussed in Chapter 2

(Narcida,1992). There are no first-cycle significant

reactivity differences between sorbent 7 and sorbent 9. This

conclusion has been confirmed using a statistical analysis

based on the method of hypothesis testing (Bethea et a l .,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 132

1975) with the confidence level of 95%. Using the same test,

sorbent 7 has a slightly higher reactivity maintenance than

sorbent 9.

5.4 Optimum Reaction Conditions

As a result of the two-cycle reaction studies, it is

possible to define the conditions at which a CaO-based high

temperature, high pressure C02 separation process should

operate:

Calcination Temperature 750°C

Carbonation Temperature 650 - 750°C

Carbonation Pressure 15 atm

% C02 in Carbonation Gas 15

Calcination should be carried out at the lowest possible

temperature (about 750°C) to minimize sorbent deterioration

and to avoid the normal operational problems associated with

higher temperature. Carbonation at 550°C should be avoided

because of the negative effect on capacity maintenance.

Carbonation at 650°C is desirable because it will permit

higher equilibrium fractional C02 removal. However, values of

the reactivity and capacity indices indicate that 750°C

carbonation temperature is also acceptable. The lack of a

narrowly defined optimum carbonation temperature may be

advantageous from the standpoint of reactor design and

control because of the exothermic nature of the carbonation

reaction.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Carbonation pressure will be dictated by the

gasification process which is likely to operate at 15 atm or

more. High pressure is favorable for high equilibrium C02

removal, and the experimental studies have shown no adverse

effect of high pressure other than a decrease in reactivity.

In a commercial process, sorbent capacity and, in particular,

capacity maintenance are more important than reactivity. The

inlet C02 mol fraction will also be determined by the

gasification process. No adverse kinetic effects of high C02

concentration have been detected, and high inlet

concentration is advantageous for high fractional C02

removal. At the most favorable carbonation conditions, namely

650°C, 15 atm, and 15% C02 in the inlet gas, the theoretical

C02 removal efficiency exceeds 99.5%.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 6

Experimental Results:

Detailed Parametric Studies

More detailed investigations of calcination and

carbonation reaction parameters are discussed in this

chapter. All previous calcination runs were carried out at 1

atm in N2. Calcination at elevated pressure has been studied

in order to investigate its effect on carbonation kinetics.

It has been shown that calcination at 900°C must be avoided

and calcination at 750°C produced the best carbonation

results. Additional runs using calcination temperatures as

low as 650°C have been carried out. The effect of low

calcination temperature on carbonation performance will be

discussed. Previous tests showed that carbonation

temperatures of 650 or 750°C produce similar carbonation

results. Additional carbonation temperatures have been

studied in order to have a more complete understanding of

this parameter. Finally, the effect of C02 concentration in

the calcination gas on the carbonation reaction is discussed.

6.1 Effect of Calcination Pressure

Figure 6.1 compares the calcination results using

sorbent 9 at calcination pressures of 1 atm (HP146) and 15

atm (HP153). The high pressure delays the start of

calcination and decreases the calcination rate by a small

134

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 135

1,000 Sorbent 9 Calcination: 750C In N2 IS ATM (HP153) -8 0 0

-600

400 TEMPERATURE, C TEMPERATURE,

// 1 ATM (HP146)

50 100 150 200 TIME, MIN.

Figure 6.1 Comparison of Calcination Kinetics at Different Pressure; Sorbent 9

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 136

amount. Nevertheless, effectively complete calcination was

achieved in a reasonable amount of time. Figure 6.2 compares

the subsequent first-cycle carbonation kinetics of sorbent 7

at 750°C, 15 atm, and in 15% C02 following calcination at 1,

5, and 15 atm. There is essentially no effect of calcination

pressure on carbonation reactivity, and little, if any,

effect on first-cycle capacity.

6.2 Effect of Calcination Temperature

It was confirmed previously that calcination at 900°C

should be avoided, and that calcination at 750°C leads to

improved carbonation performance. Lower calcination

temperatures of 700 and 650°C were studied in order to

confirm the above conclusion and to determine the minimum

possible calcination temperature. Low calcination pressure (1

atm) was required in order to achieve calcination at lower

temperature. Figure 6.3 shows the calcination curves for

sorbent 7 at lower temperatures with the 750°C calcination

results included for comparison. Temperature was increased at

a rate of approximately 5°C/min until the indicated final

temperature was reached and held constant thereafter. Minor

differences in calcination behavior were observed between 700

and 750°C, but the final step in the overall calcination

process of sorbent 7 at 650°C (decomposition of CaC03 to CaO)

was quite slow. The rate of weight loss was so slow that

after 410 minutes the rate was accelerated by increasing

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 137

1.00- sSI6*_ ^ ^ o o 0.8 0 - Calcination ah

□ 1 atm (HP036) ; 0.60- 8 o 5 atm (HP200) g a 15 atm (HP156) 0.40* D g B Sorbent 7 I Calcination: 750C, N2 i Carbonation: 750C, 15ZC02/N2,15 atm

0.00m 5 10 15 20 TIME, MIN.

Figure 6.2 Effect of Calcination Pressure on First-Cycle Carbonation Kinetics; Sorbent 7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 138

Sorbant 7 Calcination: N 2 ,1 atm 1.00

0.80

650C (HP199) Increasing N2 Flow Rate 0.60

700C (HP198)

0.40 750C (HP101)

0 100 200 300 400 500 TIME. MIN.

Figure 6.3 Calcination Kinetics as a Function of Temperature; Sorbent 7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 139

N2 flow from 300 ml/min to 500 ml/min (STP) . Complete

calcination was achieved after approximately 8% hours.

First-cycle carbonation results at 650°C, 15 atm, in 15%

C02/N2 following calcination at the three lower temperatures

are shown in Figure 6.4. The curves are almost coincident

indicating that there is little effect of lower calcination

temperature on either sorbent reactivity or capacity.

Likewise, there was little difference in the two-cycle

carbonation capacity maintenance following low calcination

temperature. Figure 6.5 shows that the values of C,2 are

effectively 1.0 at each of the three lower calcination

temperatures. Note that the adverse effect of higher

calcination temperature (825 and 900°C) which was established

in the previous chapter is included for comparison purposes.

6.3 Effect of Carbonation Temperature

The additional carbonation temperatures of 600 and 700°C

were studied using sorbent 9 following calcination at 750°C,

1 atm. Figure 6.6 shows the first-cycle fractional conversion

versus time results for five carbonation temperatures. The

time scale is limited to 20 minutes in this figure in order

to emphasize the initial rate period. All tests show the

characteristic rapid initial rate followed by the abrupt

transition to the slow rate. The initial rates at 550, 600,

and 650°C are quite similar. A slight decrease in initial

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 140

1.00- & 1 ^ ^ , 0 a ft a I s 0.80- r Calcination T«mp.: D 650C (HP199) 0 .6 0 - * 3 & o 700C (HP198) cb A 750C (HP101) t * I * Sorbent 7 0.20< Calcination: N 2 ,1 atm Carbonation: 650C, 15X C 02/N 2,15 atm

0.00 10 15 20 TIME, MIN.

Figure 6.4 Effect of Calcination Temperature on First-Cycle Carbonation Kinetics; Sorbent 7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 141

1.10

CM 1.00 o

0.90

0.80 Sorbent 7 Calcination: N 2 ,1 atm Carbonation: 650C, 1 5Z C 02 /N 2 ,15 atm

0.70 600 700 800 900 CALCINATION TEMP., C

Figure 6.5 Effect of Calcination Temperature on Capacity Maintenance; Sorbent 7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 142

1.00-

Carbonatfon Temp.

•o- 700C (HP171)

Sorbent 9 — ..... Calcination: 750C, N 2,1 atm Carbonation: 15X C 02/N 2,1 atm

TIME. MIN.

Figure 6.6 Effect of Temperature on carbonation Kinetics During Early Phases of the Reaction; Sorbent 9.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 143

rate is obvious at 700°C, and at 750°C the initial rate is

significantly lower. This result is due to the increasing

importance of equilibrium C02 pressure with increasing

temperature. At the three lower temperatures the equilibrium

C02 pressure is negligible compared to the 0.15 atm actual C02

pressure. At 700°C the equilibrium pressure is just becoming

important, and at 750°C the equilibrium pressure is

approximately one-half the actual pressure. The transition

from the rapid to the slow reaction phase occurred more

gradually at 750°C. At the lowest temperature of 550°C, the

transition occurred at lower conversion and the fractional

carbonation remained lower throughout the early part of the

reaction. However, after 40 minutes (not shown) the

fractional conversion were similar, and the capacity values

for the five tests were 0.92, 0.92, 0.96, 0.93, and 0.93 for

550, 600, 650, 700, and 750°C, respectively. Figure 6.7 shows

the carbonation temperature effect on capacity maintenance.

The capacity maintenance at 600°C lies between previously

determined values at 550 and 650°C. Similarly, the capacity

maintenance at 700°C lies between the previously determined

values at 650 and 750°C. All C,2 values in the temperature of

650-750°C range are 0.98 or above.

Figure 6.8 illustrates the effect of a still lower

carbonation temperature (450°C) using sorbent 7 following

calcination at 750°C, 1 atm, in N2. Initial carbonation rates

are similar for all temperatures. The abrupt transition to

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 144

1.10 Sorbent 9 Calcination: 750C, N 2 ,1 atm Carbonation: 15X C 02/N 2,1 atm

0.80 500 700 800600 CARBONATION TEMP.. C

Figure 6.7 Effect of Carbonation Temperature on Capacity Maintenance; Sorbent 9

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. lErESHn 1,00-| Calcination: 750C, N 2 ,1 atm Carbonation: 15XC02/N2,1 atm 650C (HP236)

550C (HP237)

450C (HP235)

T 10 20 TIME, MIN.

Figure 6.8 Effect of Temperature on Carbonation Kinetics Sorbent 7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 146

the slow rate, on the other hand, is very distinct for each

carbonation temperature. At a carbonation temperature of

450°C, the fractional conversion was about 0.20 at the

transition, and after 30 minutes the conversion only reached

0.36. This compares to transition fractional conversions of

0.52 and 0.78, and conversions of 0.88 and 0.92 after 30

minutes at 550 and 650°C, respectively. The low capacity

value at 450°C carbonation temperature is attributed to the

product layer diffusion controlling the reaction almost

immediately. The product layer diffusion coefficient is known

to be strongly temperature dependent (Bhatia and Perlmutter,

1983; DeLucia, 1985).

Figure 6.9 shows the effect of carbonation temperature

on capacity maintenance for sorbent 7 following calcination

at 750°C and 1 atm N2. Carbonation was carried out at 1 atm

in 15% C02/N2. Note that results from two tests are provided

at 550°C carbonation temperature, two at 650°C, and three at

750°C. The significant result here is that the capacity

maintenance at 450°C is less than the previously measured low

values at 550 °C. On the other hand, C12 values at the

temperatures of 650 and 750°C are essentially 1.0, in

agreement with the results for sorbent 9. Figure 6.10 shows

the effect of higher carbonation temperatures (800 and 850°C)

on capacity maintenance using sorbent 7. Calcination was

carried out at 750°C and 1 atm N2 followed by carbonation at

15 atm in 15% C02/N2. High pressure was required in order to

CAPACITY MAINTENANCE, C12 0.70 0.90 1 . 00 I I I ■ I * I 1 I ' 0 50 0 70 800 700 600 500 400 - Maintenance; Sorbent 7 Sorbent Maintenance; Sorbent 7 Sorbent acnto: 5C N2, atm ,1 2 N 750C, Calcination: abnto: XC02/ , atm 2,1 /N 2 0 C 5X 1 Carbonation: CARBONATION C TEMP., T

147 148

MO- Sorbent 7 Calcination: 750C, N 2 ,1 atm Carbonation: 1 5X C 0 2 /N 2,15 atm

o i 1.00- o uT o

1 0.90'

s 0 .8 0 -

0 .7 0 - T 500 600 700 900 CARBONATION TEMP., C

Figure 6.10 Effect of Carbonation Temperature on Capacity Maintenance; Sorbent 7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 149

achieve carbonation at the higher temperatures. Essentially

no decrease in C12 was observed at 800°C and the decrease at

850°C was relatively small. The result at 850°C, where C12 =

0.92, was superior to the result at 550°C, where C12 = 0.78.

These higher temperature results are encouraging in that they

suggest no major loss in performance for temperature

excursions of as much as 100°C above the normal maximum

temperature of 750°C. Such a margin of safety is desirable in

any exothermic reaction system.

6.4 Effect of Calcination Gas Atmosphere

Figure 6.11 shows the calcination results using sorbent

1 under different gas atmospheres. Curve A (HP048) represents

calcination in 1 atm N2. As seen in the figure, calcination

started at the temperature of approximately 610°C, and

complete calcination was achieved at approximately 730°C.

Curve B (HP079) represents calcination at 1 atm in 20% C02/N2.

Due to the the presence of C02, calcination did not begin

until 800°C and was complete in a relatively short time at

about 860°C. In Curve C (HP070) the sorbent was heated in

100% C02 to 880 °C followed by calcination in 20% C02/N2

between 880 and 900°C. In all three tests, the temperature

was held at 900°C for 20 minutes and then was cooled to 750°C

before the subsequent carbonation. Carbonation was carried

out at 750°C and 1 atm in 15% C02/N2. Figure 6.12 compares the

carbonation kinetics for the three tests. The sorbent calcined

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sorbent >600 k Hepdng and Calcination in N2 B:^Heating and Calcination in 202C02/N2 : Heating in C02 and Calcination in 20XC02/N2 (M0< I “T - -500 100 120 140 160 180 200 TIME, MIN.

Figure 6.11 Effect of Gas Atmosphere on Calcination Kinetics; Calcination at 900°C/ Sorbent 1

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 151

1.00' Sorbent 7 Calcination: 900C, 1 atm Carbonation: 750C, 15XC02/N2,1 atm 0.80<

A: Hooting and Calcination in N2 (HP048) B: Heating and Calcination in 20XC02/N 2 (HP079) C: Heating In C02 and Calcination In 20XC02/N2 (HP070)

10 15 20 25 30 TIME, MIN.

Figure 6.12 Effect of Calcination Gas Atmosphere on First- Cycle Carbonation Kinetics; Calcination at 900°C, Sorbent l

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 152

in N2 (HP048) had the highest reactivity and capacity.

Sorbents calcined in the presence of C02 experienced reduced

reactivity and capacity (HP070 and HP079). The decrease is

attributed to the fact that C02 enhances the sintering

process which causes a surface area reduction and an increase

in the pore diameter distribution.

After the first-cycle carbonation, each sorbent was

recalcined by heating to 900°C using the same gas atmosphere

as the first-cycle calcination. Second-cycle carbonation at

750°C and 1 atm in 15% C02/N2 then followed. The second-cycle

capacity decrease was more pronounced for sorbents calcined

in an atmosphere containing C02. The capacity of the sorbent

which was calcined in N2 (HP048) decreased from C, = 0.77 to

C2 = 0.57 (C12 = 0.74), while the sorbent heated and calcined

in 20% C02/N2 (HP079) exhibited a capacity decrease from Cj =

0.72 to C2 = 0.46 (C12 = 0.64). The sorbent which was heated

in 100% C02 and calcined in 20% C02/N2 (HP070) suffered a

capacity decrease from C, = 0.65 to C2 = 0.42 (C12 = 0.65).

A number of investigators have reported that the

presence of C02 during calcination at high temperature (900°C

or above) affects the structural properties of the product

CaO. Bhatia and Perlmutter (1983) reported that the pore

diameters of CaO created during calcination of CaC03 at 910°C

were increased and the distribution of pore diameters

narrowed as the C02 content of the calcination gas increased.

A reduction of surface area was also observed with increasing

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 153

C02 content. DeLucia (1985) reported that the pore volume of

CaO formed from decomposition of CaC03 at 940°C in 1 atm C02

was 27% less than the theoretical pore volume, and the pore

diameters were about 2.5 times larger than CaO formed from

decomposition of CaC03 at 800°C in N2. Borgwardt (1989b)

reported that C02 accelerated CaO sintering which caused a

reduction of surface area and porosity. Fuertes et a l . (1991)

also reported a similar effect due to the presence of C02 on

CaO at 900°C.

Figure 6.13 shows the calcination results using sorbent

1 in different gas atmospheres at 825°C and 1 atm. Curve A

(HP047) represents calcination in N2. Calcination started at

about 600°C, and complete calcination was achieved after

about 145 minutes at about 740°C. Curve B (HP081) represents

calcination in 15% C02/N2. Due to the presence of C02,

calcination started just as the temperature reached 825°C,

and complete calcination was achieved after about 180

minutes. The subsequent first-cycle carbonation results are

shown in Figure 6.14. The presence of 15% C02 in the

calcination gas decreased the carbonation reactivity, but had

essentially no effect on capacity. The first-cycle capacity

(Cj) was 0.78 and 0.79 for HP047 and HP081, respectively,

while the second-cycle capacity (C2) of HP047 was 0.60

compared to 0.58 for HP081.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 154

A (HP047)

> 0 .8 0 B (HP081)

31 s S o rtw t/1 A: HMting and Calcination In N2 B le a tin g and Calcination in 15ZC02/N2

T --- 1--- ■* 100 120 140 160 180 200 TIME, MIN.

Figure 6.13 Effect of Gas Atmosphere on Calcination Kinetics; Calcination at 825°C, Sorbent 1

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 155

1.00' Sorbent 1 Calcination: 825C, 1 atm Carbonation: 7 50 ,15XC02/N2,1 atm 0.80< A (HP047)

B(HP0B1)

k Heating and Calcination in N2 B: Heating and Calcination in 15XC02/N2

5 10 15 20 TIME, MIN.

Figure 6.14 Effect of Calcination Gas Atmosphere on First- Cycle Carbonation Kinetics; Calcination at 825°C, Sorbent l

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 156

Figure 6.15 shows calcination results using sorbent 1 in

different gas atmosphere at 750°C and 1 atm. The presence of

C02 during heating period prevented calcination at 750°C

(curve A ) . After about 150 minutes the gas was switched to N2

in order to initiate calcination, which was completed in only

about 5 minutes. Curve B (HP066) represents heating and

calcination in N2. The calcination started at approximately

600°C and was completed at about 730°C. The subsequent first-

cycle carbonation results are shown in Figure 6.16. There is

essentially no effect of calcination atmosphere at 750°C on

reactivity, and little, if any, effect on capacity. The

capacity maintenance (C12) for runs HP066 and HP065 was found

to be 0.68 and 0.69, respectively, indicating no effect of

C02 in the calcination gas at 750°C.

In summary, an adverse effect of C02 in the calcination

gas on the carbonation cycle obviously exists at 900°C.

However, At 825 °C or lower, the presence of C02 in the

calcination gas appears to have very little effect on either

capacity or capacity maintenance during subsequent

carbonation.

6.5 Conclusions

These additional tests confirm the results and trends

established in the detailed two-cycle reaction studies

discussed in the previous chapter. Carbonation temperatures

in the 650-750°C range are desirable, although periodic

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1.00 800

B (HP066)

A (HP065) -7 0 0

0.60

$ Heating and Calcination in N2

0.40 500 100 120 140 160 180 200 TIME, MIN.

Figure 6.15 Effect of Gas Atmosphere on Calcination Kinetics; Calcination at 750°C, Sorbent l

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 158

1.00

0.80

0.60

o 0 .4 0

0.20 Sorbent 1 Calcination: 750C, 1 atm Carbonation: 750, 15X C 0 2 /N 2,1 atm

0.00 0 5 TIME, MIN.

Figure 6.16 Effect of Calcination Gas Atmosphere on First- Cycle Carbonation Kinetics; Calcination at 750°C, Sorbent l

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 159

excursions to 800°C or higher seem to have no major immediate

adverse effect. Calcination temperatures as low as 700°C at

1 atmosphere appear feasible. However, the calcination

reaction is endothermic, and lower temperature excursions

must be avoided since the calcination rate becomes extremely

slow at 650°C. It is also been confirmed that the presence of

C02 in the calcination gas at 900°C affects the carbonation

cycle. However, C02 present in calcination at 825°C or lower

has been found to have little effect on either capacity or

capacity maintenance in the carbonation reaction.

High pressure calcination is feasible at a temperature

of approximately 750°C. Moreover, reactivity, capacity, and

capacity maintenance for the subsequent carbonation reaction

show no adverse effect of calcination pressure. This opens

the possibility of operating a commercial process with equal

pressures and temperatures in the carbonation and calcination

phases. Calcination can be achieved simply by reducing the

C02 partial pressure in the gas.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 7

Experimental Results:

Multicycle Studies

More detailed results on sorbent durability are

presented in this chapter. Multicyle runs were carried out in

order to extend and confirm the previous determinations of

sorbent durability through two cycles. Results of five-cycle

calcination and carbonation runs using sorbents 1, 7, and 9

are first discussed to provide direct comparisons of

carbonation reactivity and capacity throughout the cycles.

In the following sections the times used to evaluate

reactivity and capacity are changed. These changes are made

for two reasons. First, since the C02 concentration used in

most multicycle runs was significantly higher than the

equilibrium C02 concentration, the early rapid reaction phase

was almost over at (t-tc) = 1 min. The reactivity time of (t-

t0) = h min was chosen to ensure that the reactivity

comparisons were well within the rapid reaction period.

Secondly, the total time required to complete a five-cycle or

ten-cycle test needed to be reduced. Therefore, the capacity

was redefined to be the fractional conversion at (t-t0) = 20

min instead of 40 min. Since the global reaction rate in the

20 to 40 min time period is quite low, the shorter time

produces only a small change in the capacity values. It is

necessary to point out that reactivity and capacity values

160

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 161

used in section 7.1 were determined using the original values

of (t-t0) = 1 min and 40 min, respectively, since in these 1

atm tests the actual C02 pressure during carbonation was 0.15

atm compared to about 0.08 atm at equilibrium. The new time

bases are used beginning in section 7.2.

In addition to extending the tests through multiple

cycles, the effects of calcination pressure, carbonation

temperature, and background gas composition have been

investigated. Background gas composition was varied in a

step-wise manner. First, H20 was introduced into the C02-N2

gas and then a simulated coal gas containing C02, CO, H2, H20,

and N2 was tested. In the end, a small amount of H2S was added

to the simulated coal gas. In the final set of experiments,

favorable reaction conditions were selected and the tests

were extended to ten cycles.

7.1 Comparison of Sorbent Performance on Five-Cycle Runs

Five-cycle runs using sorbents 1, 7, and 9 were carried

out at the following reaction conditions: calcination at

750°C and 1 atm N2 followed by carbonation at 750°C and 1 atm

in 15% C02/N2. Figure 7.1 shows the sorbent 1 results in the

form of the raw weight-time data. Note that first-cycle

calcination data are not included in this figure. Complete

calcination was achieved in all cycles, and each carbonation

cycle exhibited the rapid initial rate followed by an abrupt

transition to a slow rate. The transition occurred at

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12-1 ; ------Sorbent 20 , Calcination: 750C, N 2 ,1 atm • Carbonation: 750C, 1 5Z C 0 2 /N 2 ,1 atm

f —r — 1 i t .i im 0 100 200 300 400 TIME, MIN.

Figure 7.1 Calcination-Carbonation Results for Sorbent Through Five Cycles

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 163

successively smaller sorbent weight in each cycle. These

results confirm the previous sorbent 1 tests where the

capacity deteriorated in the second cycle. This behavior is

similar to results of other investigators when calcium

carbonate or limestone was used as the sorbent precursor.

Figure 7.2 compares the capacity, Cif of sorbent 1 with

results reported by Barker (1973) and Delucia (1985).

Although the specific sorbents used and reaction conditions

were somewhat different in each study, the trends were

remarkably similar.

Results of five-cycle carbonation kinetics of sorbent 7

are shown in Figure 7.3. Two important results are

illustrated. First, there is a marked increase in the early

rapid reaction rate between cycles 1 and 2. Thereafter, the

reaction rate in the early stages remained approximately

constant in cycles 2 through 5. The slow stages of the

reaction exhibit a small but continuous decrease in

carbonation capacity with cycle number.

Five-cycle runs using sorbent 9 exhibit excellent

sorbent stability as shown in Figure 7.4. The initial rapid

rate is essentially equal in each of the five cycles. There

is a small decrease in capacity between cycles 1 and 2, with

essentially no decrease thereafter.

Comparisons based only on calcium utilization are

somewhat misleading because the inert MgO present in calcined

sorbent 9 reduces the C02 capacity per unit mass of sorbent.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 164

0.80< s - 20 ; ; Barfcir (1973) ^ DtLucia (1985)

0.60<

0.40-

1------1------r 2 3 4 CYCLE NUMBER

Figure 7.2 Comparison of Capacity Decrease for Sorbent l with Literature Results at similar Reaction Conditions

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 165

1.00-

Q 0 j r £ Ba S T * ® *0. 8 0 ■o 0. 0000 v v v v

■ 1st Cycle □ 2nd Cycle A 3rd Cycle

o 4th Cycle

V 5th Cycle Soitent7*86 ‘ Calcination: 750C, N 2 ,1 atm Carbonation: 750C, 15XC02/N2,1 atm

20 40 60 TIME, MIN.

Figure 7.3 carbonation Results for Sorbent 7 Through Five Cycles

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 166

1.00-

■ 1st Cycle

□ 2nd Cycle 0.6 0 - A 3rd Cycle

o 4th Cycle V 5th Cycle Sorbent 9 (HP146) 0.2C Calctootton: 750C, N 2 ,1 atm Carbonation: 750C, 15XC02/N2,1 atm

0.004 “T * — ■“ ■“ "“•"“■■T- 20 40 60 TIME, MIN.

Figure 7.4 Carbonation Results for Sorbent 9 Through Five Cycles

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 167

Figure 7.5 compares the capacities of the sorbents expressed

as grams of C02 per gram of sorbent. Data for four sorbents,

1, 7, and 9 plus a calcium magnesium acetate (CMA) obtained

from Chevron Chemical, are included. Calcined CMA is composed

of approximately 2MgO:lCaO (molar ratio).

The theoretical capacity of both sorbents 1 and 7, which

are essentially 100% CaO, is 0.79 gram C02/gram sorbent. As

shown in Figure 7.5, sorbent 7 approaches this value in cycle

1 and then experiences a slow capacity decrease in subsequent

cycles. The capacity of sorbent 1 is considerably less than

theoretical in cycle 1, and the rate of decrease in

subsequent cycles is greater than that experienced by sorbent

7. Sorbent 9, with equimolar CaO and MgO, has a theoretical

capacity of 0.46 gram C02/gram sorbent. The experimental

capacity approaches this level in each of the five cycles. As

shown in the figure, by cycle 4 the capacity of sorbent 9

exceeded that of sorbent 1. Sorbent CMA has a theoretical

capacity of 0.32 gram C02/gram sorbent. Although the measured

capacity is significantly below theoretical, the capacity

maintenance is quite good as shown by the horizontal line,

and is comparable to that of sorbent 9. This similarity

suggests that the presence of MgO is important not only for

providing open pore structure, but also for stabilizing the

structure for multicycle operation.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 168

Calclnation: 750C, N 2 ,1 atm 0 .8 0 - Carbonation: 750C, 15XC02/N2,1 atm

S-7 (HP149)

1 0 .6 0 -

3 f Eo S-9 (HP146) K ^ ( M O - 8*6 E S-1 (HP148) & 0.20-1 CMA (HP151)

T 2 3 4 5 CYCLE NUMBER

Figure 7.5 C02 Capacity per Gram of Sorbent for Four Sorbents as a Function of cycle Number

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 169

7.2 Effect of Calcination Pressure

Figures 7.6 and 7.7 show the reactivity and capacity

results versus cycle number as a function of calcination

pressure using sorbents 7 and 9, respectively. Calcination

was at 750°C in N2, and carbonation was at 650°C and 15 atm

in 15% C0 2/N2. The reactivity following high pressure

calcination was slightly lower than that following low

pressure calcination for both sorbents 7 and 9. As seen in

Figure 7.6, the capacity following high pressure calcination

appears to be more stable than that following low pressure

calcination. Figure 7.7 shows similar behavior for sorbent 9.

Figures 7.8 and 7.9 show the reactivity and capacity results

versus cycle number using sorbents 7 and 9, respectively,

using a carbonation temperature of 750°C. Otherwise, reaction

conditions were the same as shown in Figures 7.6 and 7.7.

Sorbent 7 experienced a gradual decrease in capacity with

cycle number for both calcination pressures (Figure 7.8) . The

reactivity results are similar at 750 and 650°C carbonation

temperatures. For sorbent 9, on the other hand, the capacity

was essentially constant throughout the five cycles at both

calcination pressures. Similarly, the reactivity of sorbent

9 was essentially constant over the five cycles at 750°C

carbonation temperature.

High calcination pressure has shown no serious adverse

effects on the carbonation reaction compared to low

calcination pressure. Consequently, isobaric operation with

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 170

10.60' Catenation Pncsuro: o * 15 atm (HP155) «k s ♦ 1 atm (HP157) 0.40-

§ Ri 0.20' Sorbont7 Calcination: 750C, N2 Carbonation: 650C. 15IC 02/N 2.15 atm T "■1 '"I"----- r T 2 3 4 5 CYCLE NUMBER

Figure 7.6 Five-Cycle Reactivity and Capacity of Sorbent 7 as a Function of Calcination Pressure; Carbonation at 650°C

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 171

1.00'

Ci 0.80'

£ o 0 .6 0 - Calcination Pressure:

o * 15 atm (HP154) m S 1 atm (HP163) 0 .4 0 -

§ Ri 0.20- Sorbont 9 Calcination: 750C, N2 Carbonation: 6S0C, 1 5 Z C 0 2 /N 2 ,15 atm 0.00< ■i "i" ....- - " i" T 1 2 5 4 5 CYCLE NUMBER

Figure 7.7 Five-Cycle Reactivity and Capacity of Sorbent 9 as a Function of Calcination Pressure: Carbonation at 650 °C

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 172

0.80-

0 .6 0 - Calcination Pressure: * 15 dm (HP156)

♦ 1 dm (HP162) £ 0.40-

Ri 0.20a S orbent7 Calcination: 750C, N2 Carbonation: 750C, 15ZC02/N2,15 atm 0.00< T 1 2 3 4 5 CYCLE NUMBER

Figure 7.8 Five-Cycle Reactivity and Capacity of Sorbent 7 as a Function of Calcination Pressure; Carbonation at 750°C

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 173

1.00< Ci

0.8 0 -

0 .6 0 - Caldnation Pressure

* * 1 atm (HP161) s 0 .4 0 - ♦ IS atm (HP153)

H i Ri 0.20- Sorbent 9 Caldnation: 750C, N2 Carbonation: 750C, 15X C 02/N 2,15 atm T 1 2 3 4 5 CYCLE NUMBER

Figure 7.9 Five-Cycle Reactivity and Capacity of Sorbent 9 as a Function of Calcination Pressure; Carbonation at 750 °C

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 174

sorbent regeneration accomplished via a change in temperature

and/or C02 pressure is possible.

7.3 Effect of Carbonation Temperature

High carbonation temperature (750°C) produced higher

capacity and capacity maintenance than low carbonationn

temperature (650°C). As shown in Figures 7.6 and 7.7, 650°C

carbonation temperature produced a gradual decrease in

capacity with cycle number for both sorbents. At 750°C

carbonation temperature, on the other hand, reasonably

constant capacity maintenance was found for sorbent 9 (Figure

7.9) while sorbent 7 experienced a similar trend of capacity

decrease as at 650°C (Figure 7.8).

The above results suggest that isothermal operation at

750°C through the calcination and carbonation phases would be

better than operation with the temperature cycling between

750°C for calcination and 650°C for carbonation. However,

high carbonation temperature will result in lower equilibrium

C02 removal capability. If the inlet gas contains 15% C02 at

15 atm, for example, it is theoretically possible to remove

about 99.6% of the C02 at 650°C compared to about 96.4% at

750°C.

7.4 Addition of H20 to the Carbonation Gas

The addition of H20 to the C02/N2 mixture produced an

increase in the rate of carbonation during the early rapid

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reaction phase and had a small increase in capacity. This is

illustrated in Figure 7.10 where first-cycle carbonation

results are plotted versus time. Sorbent 9 was used and

carbonation temperature and pressure were 750°C and 15 atm.

The increased rate in the presence of 10% H20 is particularly

evident in the first 1% minutes. After about 20 minutes, run

HP205 achieved a fractional conversion of 0.95 compared to

0.93 for run HP153. The addition of H20 to C02-N2 gas produced

a small but definite increase in capacity of the sorbent.

Figure 7.11 shows the capacity though five cycles number for

the same runs. Again, the capacity maintenance of sorbent 9

was quite good. Figure 7.12 shows the capacity versus cycle

number for two tests using sorbent 7. The calcination was

carried out at 750°C and 15 atm in N2, and carbonation was at

650°C and 15 atm. Improved capacity and capacity maintenance

were observed in the presence of H 20.

7.5 C 0 2 Removal from Simulated Coal Gas (H2S-Free)

The addition of CO and H2 to the previous gas

composition (C02, H 20, and N 2) provides all the major

components of coal gas. In using the simulated coal gas,

however, one must be aware of the possibility of carbon

deposition during the operation. The gas composition of 15%

C 0 2, 10% H 20, 20% CO, 10% H 2, and 45% N 2, for example, was

unacceptable to the present TGA system because of excessive

carbon deposition on the walls of the reactor and the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Carbonoffon gas eomp4

♦ t5lC02/t0Btt0/N2(HPMS) ^ 15IC02/N2 (HP153)

SorbtntO CakAnottom 750C, N 2 ,15 d m Carbondlom 750C, 15 dm

10 15 20 TIME. IAN.

Figure 7.10 First-Cycle Carbonation Kinetics of Sorbent 9 in Different Gas Atmospheres

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1.00-

8 0 .9 0 - c5

1 0 .8 0 - Sorbent 9 Caldnation: 750C, M2,15 atm Carbonation: 750C, 15 atm

0.70- 15IC02/10XH20/N2 (HP205) 15XC02/N2 (HP153)

T 2 3 4 5 6 CYCLE NUMBER

Figure 7.11 Five-Cycle Capacity of Sorbent 9 as a Function of Carbonation Gas Atmophere

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 178

1.00

Sorbent 7 Calcination: 750C, H2, IS atm Carbonation: 650C, 15 atm

0.70 • 15XC02/10ZH2O/N2 (HP209)

0.60 0 1 2 3 4 5 6 CYCLE NUMBER

Figure 7.12 Five-Cycle Capacity of Sorbent 7 as a Function of Carbonation Gas Atmosphere

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 179

hangdown wire. The sorbent itself appeared to be free of

carbon. Thermodynamic analysis of carbon deposition tendency

(Lamoreaux et a l ., 1986) predicted that the problem would be

most severe as the reactive gas was heated to final reaction

temperature, but less important once reaction temperature was

reached. This is in agreement with the observed location of

carbon deposited in the side stream heating line, the insert

tube inside the reactor, and the upper hangdown wire.

The ratio of C/(0+H) for the above composition was 0.438

indicating a strong possibility of carbon deposition.

Increasing the H20 content to totally eliminate the

possibility of carbon deposition was impossible for the

current electrobalance system. A gas composition of 5% C 0 2,

10% H 20, 5% CO, 2.5% H2, and 77.5% N2 was selected as an

alternate. Although this composition did not completely

eliminate carbon deposition (C/(0+H) = 0.33), it reduced the

quantity of carbon deposited on the hangdown wire to a level

small enough that it did not confound the kinetic results.

The simulated coal gas created the possibility of the

simultaneous occurrence of the water-gas shift and

carbonation reactions:

C 0 <*> + *2 0(g) - C02(g) + H2(g) (7-1)

and

^^(s) + C02(g) ** CaC02 (S j (7—2)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 180

While no direct confirmation of the simultaneous reactions is

possible using the electrobalance reactor, the previous

atmospheric electrobalance tests (see Chapter 4) showed an

increase in carbonation rate which would be consistent with

higher concentration of C02 formed by water-gas shift. Figure

7.13 shows the fractional carbonation-time results for the

first carbonation cycle for three runs with different feed

gas compositions. All runs were subjected to calcination at

750°C and 15 atm in N2 and carbonation at 750 and 15 atm. The

results of run HP222 where the carbonation gas consisted of

5% C02/N2 were taken as a base case for comparison. The

addition of 10% H20 in run HP224 produced a clear increase in

carbonation rate. This is consistent with the previously

discussed promotional effect of H20 on carbonation rate. The

highest overall carbonation rate was associated with run

HP218 using feed gas composition of 5% C 0 2, 10% H 20, 5% CO,

2.5% H2, and 77.5% N2. The duration of the rapid initial

reaction period was also longer for this run. Sorbent

capacity, C,(20), was effectively the same in all runs.

The increased reactivity of HP218 compared to HP224 is

taken as further evidence of the probable simultaneous

occurrence of the carbonation and water-gas shift reactions.

The presence of CO and H2 in the HP218 carbonation gas

provides all components necessary for the shift reaction to

occur. This result is consistent with similar observations

discussed in Chapter 4.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 181

1.00-

□ □ a □ 0

o a o 2 Carbonation Gas Comp.:

o & □ 5ZC02/N2(HP222)

a 5XC02/10ZH20/N2(HP224) o 5XC02 /1 0ZH2O/5ZCO/ 2^ZH2/N2 (HP218)

Sorbent 9 Calcination: 750C, N 2 ,15 atm Carbonation: 750C, 15 atm "T »" -I 1 T 10 15 20 25 TIME, MIN.

Figure 7.13 First-Cycle Carbonation Kinetics of Sorbent 9 using Three Different Gas Atmospheres

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 182

7.6 C02 Removal from Simulated Coal Gas (With H 2S)

H 2S present in the simulated coal gas reacted

competitively with C02, thereby reducing the carbonation

capacity. In addition, the sulfidation reaction was

irreversible under the conditions of interest so that, in a

relatively short time, the entire sorbent was converted to

CaS and no C02 removal was possible.

Figure 7.14 shows the normalized sorbent weight, W/W0,

against time of run HP226 using the simulated coal gas with

0.22% H2S in the carbonation cycles. Zero time corresponds to

the beginning of the first carbonation cycle; the first

calcination cycle is not included in this figure. During the

early stages of the first carbonation cycle the sorbent

weight increased rapidly due to the simultaneous reactions

(7-2) and

C a 0 (s) + H 2 S (g) ** CaS(s) + H2°(g) ( 7 _ 3 )

A maximum value of W/Wo « 0.75 was achieved after about three

minutes. Thereafter, W/W0 decreased due to the displacement

of carbonate by the reaction

C a C 0 3(s) + H z S ( g ) ** Ca S (s) + H2°(g) + ^ 2 [ g ) (7 _ 4)

This reaction and the resultant sorbent weight loss continued

until the reactive gas flow was stopped after about 30

minutes. In the 40 to 55 minute time period the remaining

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 183

Sorbont 9 (HP226) Calcination: 750C, N2, IS atm Carbonation: 750C, 15 atm . 5ZC02/ 10ZH2O/5XC0/ 2.5ZH2/0.22ZH2S/N2

100 150 TIME. MIN.

Figure 7.14 Weight-Time Response during Multicycle Carbonation of Sorbent 9 with H2S in the Reacting Gas

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CaC03 was decomposed by calcination in N2. However, the final

value of W/WQ « 0.58 suggests that more than 50% of the

calcium had been irreversibly converted to CaS during the

first reaction cycle. The second carbonation cycle was

initiated at 70 minutes and the maximum value of W/WQ

achieved was 0.68. The early weight increase was again due to

the simultaneous sulfidation and carbonation reactions. After

reaching the maximum, W/W0 decreased from 0.68 to 0.63, again

due to the displacement of carbonate by sulfide. Third-cycle

calcination in N2 resulted in a reduction of W/W0 to 0.61,

which suggested that approximately 90% of the calcium had

been converted to CaS. Very little weight gain occurred in

the third carbonation/calcination cycle since only a small

fraction of calcium remained in the reactive CaO form. By the

end of the third cycle, about 98% of the calcium had been

irreversibly converted to CaS.

Much of the loss of carbonation capacity in run HP226

was due to the replacement of carbonate by sulfur after the

maximum value of W/W0 was achieved. Similar runs were carried

out using sorbents 7 (HP230) and 9 (HP229) in which the

carbonation cycles were terminated just after the maximum

weight was achieved. Although appreciable carbonation

capacity was maintained throughout the four cycles,

continuing capacity decrease with cycle number was evident

due to the competitive formation of CaS. Figure 7.15 shows

the increase in the estimated percent of calcium converted to

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 185

100

HP226 (S -9)

HP230 (S-7)

HP229 (S-9) o

20- Calcination: 750C, N 2 ,15 atm Carbonation: 15X C 02/N 2,15 atm , 5XC02/10XH20/5XCO/ 2.5XH2/0.22IH2S/N2

0 2 3 4 5 CYCLE NUMBER

Figure 7.15 Build-Up of Calcium Sulfide during Carbonation Cycles

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 186

CaS following-each cycle for runs HP229 and HP230. Results

from HP226 are included for comparison. Sorbent 7 appeared to

be even more susceptible to CaS formation than did sorbent 9.

Even with the reduced carbonation cycle time, from 50 to 60%

of the calcium was irreversibly converted to CaS after four

cycles.

It appears, therefore, that prior desulfurization will

be required if the CaO sorbent is to be used for many cycles

of C02 removal.

7.7 Ten-Cycle Runs Using Simulated Coal Gas (H2S-Free)

Figure 7.16 shows the fractional carbonation-time

results for the first, fifth, and tenth carbonation cycles of

sorbent 7 (HP232) . Calcination was at 750°C and 15 atm in N2,

and carbonation was at 750°C and 15 atm in 5% C 0 2, 10% H 20, 5%

CO, 2.5% H2, and 77.5% N2. The sorbent showed little change

in initial reactivity, but the transition point between rapid

and slow reaction phases occurred at successively lower

values of fractional carbonation as the number of cycles

increased. This shift in the transition level prompted a

decrease in capacity with increased cycle number.

Figure 7.17 illustrates the carbonation capacity versus

cycle number for four runs using sorbent 7. Results from

earlier five-cycle runs, HP206 and HP221, at the same

conditions as HP228 and HP232, respectively, are included for

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -B - l i t Cycle

-o -5 th Cycle

-a - 10th Cycle

Sorbent 7 (HP232) Calcination: 750C, N 2 ,15 atm Carbonation: 750C, 15 atm . 5XC02/10XH2O/5XCO/2.5XH2/N2 « . » V T .... I I' '|" l 1 l-l-pi'TTTTTTI-P* 0 5 10 15 20 25 TIME, MIN.

Figure 7.16 Carbonation Kinetics of Sorbent 7 in the First, Fifth, and Tenth Cycles

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1.10

1.00 HP206

HP221

HP232

Sorbont7 Calcination: 750C, N 2 ,15 atm Carbonation: 750C, 15 atm HP228 0.70

♦ 5XC02/10XH2O/5XCO/2.5XH2/H2 0.60 0 1 2 3 4 5 6 7 8 9 10 CYCLE NUMBER

Figure 7.17 Carbonation Capacity Versus Cycle Number for Ten-Cycle Runs Using Sorbent 7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 189

comparison. In the simulated coal-gas atmosphere (5% C02, 10%

H20, 5% CO, 2.5% H2, and 77.5% N2) the five-cycle results from

HP221 match the ten-cycle results from HP232 quite well. The

capacity decrease over the ten-cycle test was less than 10%.

In the simpler test gas containing no CO and H2, performance

during the ten-cycle run (HP228) was poorer than in the

previous five cycle run (HP206). The first-cycle capacities

were essentially indentical but HP228 sufferred significant

capacity loss in each subsequent cycle; the capacity

decreased by about 30% from the first to the tenth cycle. All

other replicate tests produced much better agreement, and no

reason for the lack of reproducibility in these two runs is

known.

Sorbent 9 has shown better capacity maintenance than

sorbent 7. Figure 7.18 shows the fractional carbonation-time

results for the first, fifth, and the tenth cycles using

sorbent 9 (HP231). The same operating conditions as those of

sorbent 7 previously described were used. The curves for the

three cycles were essentially identical suggesting that

sorbent 9 maintains superior reactivity and capacity

throughout ten cycles. Figure 7.19 illustrates the

carbonation capacity versus cycle number for four runs using

sorbent 9. The results from two five-cycle and two ten-cycle

runs at the same conditions are shown. In this case, the

results for all four tests are quite comparable, and the ten-

cycle runs show good capacity maintenance, in contrast to

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. *b * 1st Cycle -o- 5th Cyd«

•a * 10th C ydt

Sorbent 9 (HP231) Coleinoffon: 750C, H 2 ,15 atm Carbonation: 750C, 15 atm , 5ZC02/10ZH20/51CO/2^2H2/N2

0 5 10 15 20 25 TIME, MIN.

Figure 7.18 Carbonation Kinetics of Sorbent 9 in the First, Fifth, and Tenth Cycles

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 191

1.10 3o rb#n t9 Calcination: 750C, N 2 ,15 atm Carbonation: 750C, 15 atm

1.00- HP205 HP218 HP231 § £ 0 .9 0 - HP227

3 .

0 .8 0 - 5SC02/10ZH20/53C0/2.5ZH2/N2

5XC02/10ZH20/N2

0 .7 0 + ' 1 t 1 i i ■”! " i r ■■ i i -r"-" 0123456789 10 CYCLE NUMBER

Figure 7.19 Carbonation Capacity Versus Cycle Number for Ten-Cycle Runs Using Sorbent 9

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 192

sorbent 7. In HP231 the capacity in the tenth cycle was only

1% lower than in the first cycle. In HP227 the capacity

values for the first and the tenth cycles differed by

approximately 3%.

7.8 Conclusions

Multicycle runs using sorbents 1, 7, and 9 have been

carried out in order to extend the understanding of the

durability of the sorbent. Sorbent 1 was found to posses the

lowest reactivity maintenance and capacity maintenance after

being subjected to five-cycle runs. Sorbent 7 had the highest

calcium utilization in the first cycle, but experienced a

gradual decrease in capacity with increasing number of

cycles. Sorbent 9 was the best sorbent in term of reactivity

maintenance and capacity maintenance.

The addition of steam to the carbonation background gas

produced an improvement in sorbent reactivity, capacity, and

durability. Further addition of CO and H2 to produce a

sulfur-free simulated coal-gas had no significant effect on

the kinetics of the carbonation reaction. However, careful

choice of gas composition was required in order to avoid

carbon deposition in the reactor. Addition of H2S caused a

rapid and irreversible deterioration in carbonation capacity

because of the irreversible reaction (7-3). In addition, H2S

was capable of displacing previously formed carbonate by

reaction (7-4) . Since CaS could not be reconverted to CaO, it

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. appears that a prior desulfurization step will be required

before the calcium-based sorbent process can be used

commercially for bulk removal of C02.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 8

Application of Pore Models with

Structural Changes to the Carbonation Reaction

The reaction of interest is:

C CaC03{g)

The differences in molar volumes of reactant CaO (16.8

cm3/mol) and product CaC03 ( 36 . 9 cm3/mol) cause structural

changes in the solid during the reaction. It has been shown

from the TGA studies that the reaction occurred in two

distinct phases: an early rapid reaction phase was followed

by an abrupt transition to a slow reaction. During the slow

phase, the reaction effectively stopped well before the

theoretical maximum conversion was reached.

In order to describe the experimental results, a model

which accounts for structural property changes during the

reaction is required. The distributed pore size model

developed by Christman and Edgar (1983) has been chosen for

the modeling effort. The model provides for an evolution of

pore size distribution in the solid as the reaction proceeds.

The model accounts for four resistances: mass transfer of the

reactive gas to the exterior of the particle, diffusion of

gas in the pores, diffusion of gas through the product layer,

and surface reaction.

194

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 195

This chapter begins with a brief derivation of the

distributed pore size model which is adapted directly from

Christman and Edgar (1983). The parameters required as input

to the model are then discussed. Model predictions are then

compared to the experimental data.

The model is only applied to the experimental data for

sorbent 1 since the structural characteristics of that

sorbent are better defined and the incomplete conversion was

most noticeable for that sorbent. The model predictions are

compared with the experimental data using sorbent structural

properties determined from the mercury pore size distribution

of Narcida (1992) .

8.1 Distributed Pore Size Model

Consider the noncatalytic gas-solid reaction:

Pl-fys) + P2C (sr) P3S(s) + P^fgr)

The following assumptions are made:

(i) The solid reactant A is a porous spherical

pellet having an initial radius of Rq which remains

constant throughout the reaction.

(ii) The porous medium is made up of a

distribution of open, interconnecting, cylindrical

pores with a random distribution of orientations

and locations.

(iii) Isothermal conditions prevail.

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(iv) The reactive gas concentration is a function

of time and radial position in the pellet.

(v) The net mass flux of gas is neglected.

(vi) The pseudo steady state assumption for the

gas concentration profile in the pellet is

applicable.

Equations describing the diffusion of reactive gas

through the product layer and the chemical reaction taking

place on the product-reactant interface are first derived.

The evolution of the pore size distribution is then

discussed. Finally, by integrating the pore size

distribution, the macroscopic properties necessary to obtain

the pseudo steady state gas concentration in the pellet will

be presented.

8.1.1 Chemical Reaction in a Single Fore

Consider a single pore with initial radius r0. The

reaction is assumed to obey the unreacted core model. During

the reaction a product solid will accumulate on the walls

between the pore and the product-reactant interface with a

thickness of (r2-r,) as shown in Figure 8.1. It is assumed

that the length of the cylindrical pore under consideration

is small enough that the gas concentration C has the same

value throughout the pore length, 1.

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reactant A reactant A

Figure 8.1 Geometric Changes During Reaction in a Single Pore (Christman and Edgar, 1983)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 198

By assuming a first order reaction with respect to

reactant gas, and performing a mass balance throughout the

product layer, we obtain the gas concentration at the

reaction interface, C(r2), as

C(r9) = ------1 + r2(-£) l n ( ^ ) (8_1) D b rx

where C is the gas concentration in the pore in mol/cm3, k is

the surface reaction constant in cm/s, and Ds is the

diffusivity of gas through the product layer in cm2/s.

As the reaction proceeds, rj and r2 will change. It is,

therefore, necessary to express r, and r2 as a function of

time. The rate of change of r2 is calculated from

[l t ]'o = {Y 2] VAk C ^2) (8-2)

where VA is the molar volume (cm3/mol) of solid reactant A.

Substituting Eq.(8-1) into Eq.(8-2) gives

. (-£±) VAk C (8-3) i ♦ r 2 Ds

The relationship between r, and r2 is based upon the

conservation of mass of solid A:

xl = a r02 + (l-a) r22 (8“4)

where

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a is the ratio of the molar volumes of the solid product and

reactant, VB/VA, and the stoichiometric coefficients,

Taking the derivative of Eq. (8-4) and applying Eq. (8-3) gives

, (-|i) vh k (1-a) ( i ) C t £ l , . ■ ^ (3-6, 3C '• i ♦ r2 if) in(i 2 D. r.

(dr,/3t) in Eq. (8-6) depends on both r, and r2, and gas

concentration, C. Moreover, gas concentration C is a function

of both time and radial position, R, within the pellet.

In order to eliminate the dependence of C on and r2,

a new parameter t is introduced as

x = f £{Rj_tI dt (8_7) J Cn

where C0 is the gas concentration at the surface of the

pellet (R=Ro) . r is called the cumulative gas concentration

first introduced by Dudukovic (1976). Note that r has the

same value as time t if there is no pore diffusion

resistance. By differentiating Eq.(8-7) with respect to time

and using the chain rule for Eq.(8-6), we obtain

a (-I1*VA k (i-K) < — ) C0 . _ L _ J (8-8) a t 1 + r 2 i f ) i n i f )

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 200

Eq.(8-8) can be combined with (8-4) to obtain an expression

for (3r,/dt) that depends only on t and r,. Integrating this

equation using the initial condition r, = r0 at r = 0 yields

x = -(1~“)r°Xk { i-t a-i T “ l} + (ttIt) 4 XDg — rQ )2 ln( r0 ^)2

T ^ 2 ( — > (8-9) - ((£i) - a) in [— 5“---- ] } rn 1 -a

where

A = (ii) VA (a-1) C0 (8-10) P2

Eq.(8-9) is an analytical expression which relates t to r,

and r0.

8.1.2 Evolution of Fore Size Distribution

In a spherical pellet, there exists a distribution of

pores which intersect the surface of the sphere located at R.

The distribution is defined by a distribution function

^(r^RjtJdr,, which is the number of pores per unit surface

per unit radius of cyclindrical pore with sizes between r,

and (rj+dr,) . It is assumed that the pores are randomly

oriented in the porous matrix independent of size r, and that

the average length 1 of the pores is small with respect to

the radius of the pellet.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 201

The population balance over the pore size distribution

generates the following equation (in term of t)

arMr^T) A d [ { } _ Tx 3rx J

«.<*,.*> d v U £ R ’X)- (8-ID

where (d

in the number of pores due to pore intersections. For

simplicity, the model assumes that there are no pore

intersections during the reaction. Eq.(8-11) is then

simplified to

8.1.3 Chemical Reaction in Porous Medium

The macroscopic properties of the porous medium are

obtained by relating the properties of individual pores to

the pore size distribution. The void area per unit area xp is

oo i|f = Jn rx2 T)! dr1 (8-13) o

For randomly oriented pores, the void area per unit area is

equal to the void volume per unit volume (Petersen, 1957;

Schechter and Gidley, 1969), and, therefore, the porosity e

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 202

e = Jn rx2 dz1 (8-14)

Gas concentration profiles within the pellet are

determined by performing a mass balance on reactant gas C

undergoing diffusion and chemical reaction in a spherical

porous pellet

i d s - * c (8- 15)

where

D, = lyudr, (8-16) ’ 0

K = 2k 1 ^ J tr r 1 (8-17) 0 l + r2 (— ) In (— ) Ds r±

D* ‘ (irAB * U K ^ Z 1 > (8‘18>

f is a tortuosity factor (dimensionless), DAB is the bulk

diffusivity of the gas mixture, cm2/s, DK is the Knudsen

diffusivity, cm2/s, and De is the effective diffusion

coefficient, cm2/s. Note that De in Eq. (8-15) is a function of

both time and location since it depends on the pore size

distribution r/(R,t). Similarly, Ke depends on the pore size

distribution 77 (R,t) . The boundary conditions required to

solve Eq.(8-15) are

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 203

-|§ = 0 at R = 0 (8-19)

De 'If = k* (C° “C) at * = ^ (8"20)

where kg is the mass transfer coefficient, cm/s.

The local conversion is expressed as

x(R,t) = (8-21) (l-e0) (a-1)

The rate of change of local conversion with time is obtained

directly from the equivalent reactivity Ke as

dx _ ,P1} VAKeC (p-”) a t (8 22)

The overall porosity, conversion, and reaction rate are

determined using a volume-weighted integration over the local

property of interest. The overall conversion, X(t), for

example, is determined from the local conversion, x(R,t), as

*'0 x(t) = — ^—-[a % R 2 x (R) dR (8-23) o

The overall conversion, X(t), may then be compared to the

experimental data.

8.2 Numerical Solution Technique

The model must be solved numerically. Figure 8.2 shows

a flow chart of the solution procedure taken from Christman

(1981).

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distribution value of r0 value of the In discretized size pore discretized Generate aTable of r as a function of tas aeach function for Check^\^ No spline interpolation spline ^ ^ a n y point values of r1 values r1 of and x local rate local has changed v. v. at significantly ^ / thesee to if ^ values of x(R) cubic by Ke and . thee new from to determine n^ to determine atn^ discrete Solve the population balance Solvethe population Determine newofvalues D e ,

Yes Printout Initial Initial Pore Results Discretize the Discretize Intermediate Size Distribution

of D e and K s

at each grid point at each grid to determine determine to x (R) Calculate the gasCalculate

centration over time centration concentration profile concentration using the newvalues using Integrate the gas Integrate con size distribution to sizedistribution tau of asa function obtain Dobtain e . Kgand e Integrate over the pore overIntegrate

Initial SizePore Initial / Read Model in Distribution Distribution /

/ Parameters the and

Check^\^

to seeto if No

termination time has termination ^ been reached , change in thetotal change in conversion (DELX)conversion Figure Figure 8.2 Flowchart for the Distributed Pore Size Model Calculate aCalculate time step (DELT) give ato small START Yes Calculate the initial gas the Calculate initial concentration profile by profile concentration solving the pseudo the steadypseudo solving initial values of values Deand Keinitial state mass balance using the state mass balance using END

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(1) Initially, all model parameters and the initial pore

size distribution are input.

(2) The pore size distribution is then internally

discretized into approximately 50 divisions with a constant

value of tj, over each interval.

(3) Using Eq.(8-9) a table of rj as a function of r, for

each value of r0, is generated.

(4) The population balance (Eq.(8-12)) is used to

determine rj, at discrete values of rx and t.

(5) The macroscopic properties (De, Ke, and e) are then

tabulated at 100 values of t by integrating over the pore

size distribution using Eqs.(8-16), (8-17), and (8-14).

Gauss-Legendre quadrature is used because r is not a

constant step size.

(6) A cubic spline is fit through all tabulated values

for the purpose of interpolation later in the program.

(7) The initial gas concentration is obtained by solving

Eq.(8-15) using a centered finite difference method giving a

set of linear equations in local gas concentration which are

solved using the tridiagonal matrix technique.

(8) Time is incremented by determining the time required

to produce a specified small change in the total conversion.

This is done by the following:

(8a) Integrate the gas concentration profile over time

using the trapezoidal rule to determine a value of t at each

grid point (Eq.(8-7)).

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(8b) From the new value of t the new values of De, Ke,

and e are determined using a cubic spline interpolation.

(8c) The local rate of reaction (KcC) is compared to its

previous value at each point. If the local rate of reaction

at any point has changed by more than a prespecified limit,

the gas concentration is then calculated (Eq.8-15) using the

new values of De and Ke (from step (8b)) and the procedure is

repeated from step (8a) through step (8c).

(8d) If the change in the local rate of reaction at any

point is less than the prespecified limit (i.e. convergence

has been achieved), intermediate results are printed out. The

results include the values of overall rate, conversion, and

porosity which are calculated by integrating over the local

values of these properties using Simpson's rule.

(9) A new time step is initiated and steps (8a) through

(8d) are repeated until the desired total reaction time is

reached or the pores at the outer shell of the pellet are

plugged.

Before comparison with the experimental data, the

program code was first validated by matching cases reported

by Christman and Edgar (1983).

8.3 Model Parameters

The parameters required as input data for the

distributed pore size model are summarized in Table 8-1, and

are discussed below.

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Table 8-1

Model Parameters Used for

Distributed Pore Size Model

Symbol Parameter. Units

Ro Particle Radius, cm

a Ratio of Molar Volumes of Product (VB)

and Reactant (VA)

k Reaction Rate Constant, cm/s

Dab Bulk Diffusivity, cm2/s

Dk Knudsen Diffusion Coefficient, cm/s

Ds Product Layer Diffusivity, cm2/s

f Tortuosity Factor

K Mass Transfer Coefficient, cm/s

C0 Effective Bulk Reactive Gas

Concentration, mol/cm3

ft Stoichiometric Coefficient of

Component i

Mass Density of Solid Reactant, g/cm3

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(1) Physical Properties of Crystalline Solids

The molar volumes of CaO and CaC03 are 16.8 and 36.9

cm3/mol, respectively, giving an expansion ratio, a, of 2.20.

The true mass densities of CaO and CaC03 are 3.345 and 2.71

g/cm3, respectively. These values are taken from Handbook of

Chemistry and Physics (Weast, 1989).

(2) Particle Radius

The particle size of the initial solid CaO was

determined from the SEM studies of Narcida (1992). The CaO

particles were produced by calcination of CaC03 at 750°C and

1 atm in N2 for 1 hr. The initial CaC03 particles were

approximately cubical in shape with the particles ranging

from 0.5 to 10 /im as determined from SEM photomicrographs.

Using the BET surface area of 0.9 m2/g (Narcida, 1992) and

solid density of 2.71 g/cm3, the average length of the

cubical particles was calculated to be 2.5 jtim. The mercury

porosimetry tests of precursor CaC03 indicated effectively

nonporous particles (see Chapter 2) . From the SEM results,

the particles remained cubical in shape after calcination,

but a rough surface was observed suggesting that pores were

created during calcination.

The particle radius used as a parameter in this model

was determined using the equivalent radius of a sphere whose

volume is equal to the volume of cubical CaO having length of

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1 . With the length of 2.5 jtzm the equivalent radius was

calculated to be 1.55 /zm.

(3) Pore Size Distribution

Pore size distribution is one of the very important

parameters required in this model. This parameter plays an

important role in describing the evolution of structural

properties during the reaction. The sudden reaction "die-off"

predicted by an average pore size (for example, Bhatia and

Perlmutter, 1980, 1981) does not occur with a pore size

distribution.

The mercury porosimetry results of Narcida (1992)

summarized in Table 8-2 were used. Most of the pore volume

corresponds to pore diameters ranging from 0.02 to 0.09 /xm

with a small additional pore volume in the pore diameter

range of 0.003 to 0.01 jum. The total pore volume of 0.3629

cm3/g corresponds to an initial porosity of 0.548. This is

quite close to the theoretical porosity of 0.545 which would

be produced by calcination of nonporous CaC03 at conditions

where no sintering occurred. Note that the model will convert

from the pore diameter, as shown in Table 8-2, into the pore

radius for further calculations.

(4) C02 Gas Concentration

The carbonation reaction is assumed to be first order

with respect to reactant gas concentration. At the

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Table 8-2

Cumulative Pore Volume as a Function of Pore Diameter for Sorbent 1 (Narcida, 1992)

Pore Diameter Cumulative Pore (urn)_____ Volume (cm3/q)

0.0907 0 0.0804 0.0029 0.0724 0.0109 0.0656 0.0292 0.0604 0.0498 0.0519 0.1070 0.0402 0.2100 0.0363 0.2357 0.0303 0.2601 0.0259 0.2674 0.0227 0.2711 0.0202 0.2731 0.0181 0.2753 0.0130 0.2780 0.0101 0.2839 0.0091 0.2879 0.0065 0.3001 0.005 0.3121 0.004 0.3247 0.003 0.3629

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temperatures of interest, the equilibrium C02 pressure is

significant at low total pressure. Therefore, the effective

bulk reactant gas concentration, C0, is taken to be the

difference between the actual bulk C02 concentration, Cb, and

the equilibrium C02 concentration, C^. Assuming ideal gas

behavior, the "effective” gas concentration, C0, is therefore

C = ^ co2 Peg _ VcojP Peg (8—24) 0 RT RT

At 650°C, for example, the equilibrium C02 pressure is 0.01

atm. With 0.15 mol fraction of C02 in the reactant gas at 1

atm total pressure, the effective C02 concentration is 1.85E-

06 mol/cm3.

(5) Surface Reaction Rate Constant

Bhatia and Perlmutter (1983) estimated the rate constant

for the carbonation reaction by applying the random pore

model (Bhatia and Perlmutter, 1980; 1981) to their

experimental data during the rapid reaction phase. The

intraparticle and transport resistances were reported to be

negligible in that phase. The average value of the rate

constant was found to be 0.0595 + 0.0018 cm4/(gmole)(s) in

the temperature range of 550 to 725°C. The lack of

temperature dependence suggests that the value is only

approximate. No other literature values of the carbonation

rate constant are known.

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Note that the units of the rate constant reported by

Bhatia and Perlmutter (1983) are different from the units

used in this model. Bhatia and Perlmutter's value of 0.0595

cm4/ (gmol) (s) may be converted to 0.00354 cm/s by dividing by

the molar volume of CaO. This value will be used as a guide

before being treated as a best-fit parameter.

(6) Molecular and Knudsen Diffusivity

Molecular diffusivity of C02 in N2 was determined using

the Chapman-Enskog equation (Bird, Stewart, and Lightfoot,

1960)

T 3(— +— ) M a M b (8-25) Dm = 0.0018583 p o AB 2 Q D,AB

where DAB is the molecular (or bulk) diffusivity in cm2/s, T

is the temperature in K, MA and MB are molecular weights of

species A and B, respectively, p is the pressure in atm, aAB

is the Lennard-Jones parameter in A, and flDAB is a

dimensionless function of temperature and of the

intermolecular potential field for one molecule of A and one

of B. Parameters needed to evaluate ctab and nDAB are tabulated

(Bird, Stewart, and Lightfoot, 1960) . For the C02-N2 system at

650°C and 1 atm, for example, aAB is calculated to be 3.838,

and nDAB to be 0.7896 giving the molecular diffusivity DAB to

be 1.08 cm2/s.

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The Knudsen diffusivity is a linear function of pore

radius given by (Froment and Bischoff, 1990)

If1'1 (8-26)

where DK is in cm2/s, R is the gas constant in

kg.m2/ (s2) (K) (mol) , T is the temperature in K, r is the pore

radius in cm, and MA is the molecular weight of species A.

For an average pore radius of 0.02 jum, for example, the

Knudsen diffusivity of C02 at 650°C is 0.089 cm2/s.

The effective diffusivity is the combination of

molecular and Knudsen diffusivities according to Eq.(8-18).

With an average pore radius of 0.02 jum the effective

diffusivity at 650°C and 1 atm is 0.082 cm2/s showing that

Knudsen diffusion is the most important diffusion mechanism.

At high pressure, however, both mechanisms are important. For

example, at 650°C and 15 atm, Dad = 1.08/15 = 0.072 cm2/s

while Dk = 0.089 cm2/s, giving De = 0.040 cm2/s.

(7) Tortuosity Factor

The tortuosity factor accounts for non-ideality in pore

orientation, shape, and interconnectiveness. This value is

expected to vary with pore size distribution in order to

obtain the correct diffusional resistance through the porous

matrix and the correct concentration profile in the pellet.

If pore diffusion resistance is not important, however, the

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model is not sensitive to the value. A tortuosity factor of

3, which is within the range reported by Satterfield (1970),

has been chosen in all cases.

(7) Product Layer Diffusivity

Values of the product layer diffusivity reported in the

literature vary significantly. Bhatia and Perlmutter (1983)

applied the random pore model to estimate the "effective"

product layer diffusivity (Dpc) for the carbonation reaction.

Dpe was defined as DpCsMCa0/pCa0. Dp was the solid state

diffusivity, Ca the diffusing species concentration

(unknown) , MCa0 the molecular weight of CaO, and pCa0 the mass

density of CaO. The activation energy was found to be 21.2

±0.9 kcal/mol over the temperature range of 400 to 515°C and

42.8 ± 1.7 kcal/mol over 515 to 725°C. At 650°C, Dpe was found

to be 1.0E-14 cm2/s. Assuming that solid CaC03 was the

diffusing species (C5 = 0.0271 mol/cm3) , the solid state

diffusivity is, therefore, 2.2E-14 cm2/s.

Anderson (1969) studied the diffusion of carbon and

oxygen atoms in the calcite lattice. Calcite crystals were

used in contact with a gas reservoir of isotopic C02. By

measuring the change in the isotopic concentration in the gas

reservoir, he concluded that over the temperature range of

550 to 850°C the self-diffusivity of the carbon atom was

D cazbon = 1 ■ 3E+03exp (-88 (kcal/mol) /RT) (8-27)

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where Dcarbon is in cm2/s. At 650°C, Dcarbon = 1.90E-18 cm2/s. The

oxygen self-diffusivity was found to be higher by a factor of

four. Kronenberg et al. (1984) reported an activation energy

of carbon self-diffusivity in the calcite crystals to be 87

± 2 kcal/mol over the temperature range of 500 to 800°C. The

carbon self-diffusivity at 650°C was 1.63E-18 cm2/s, in

agreement with Anderson (1969).

Mess (1989) reported the effective diffusion

coefficient, Deff/ of the carbonation reaction at high

temperatures (> 900°C) and longer times (> 600 minutes) as

Deff = 0.65 exp (-56.9 (kcal/gmol) /RT) (8-28)

where Dcff is in cm2/s. Deff in Eq. (8-27) is, in principle, the

same as the product layer diffusivity, Ds, discussed in this

section except that Dcff was based on single crystal particles

with no grain boundaries. At lower temperatures (< 850°) and

short times, however, the Dcff values were not reported.

The product layer diffusivity is generally treated as an

adjustable parameter in modeling gas-solid reactions. Lew et

al. (1992b), for example, used the overlapping grain model

(Sotirchos and Yu, 1988) and reported an activation energy of

26.4 kcal/mol for product layer diffusivity over the

temperature range from 400 to 700°C for the ZnO + H2S

reaction. At 650°C, the product layer diffusivity was 5.50E-

08 cm2/s. In comparison, Ranade and Harrison (1981) applied

the modified grain model to describe the ZnO + H2S reaction

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and an activation energy of 22 kcal/mol was reported. A

product layer diffusivity of 3.0E-09 cm2/s was calculated at

650°C, about an order of magnitude lower than the value

reported by Lew et al. (1992b).

Variation in the values of product layer diffusivity are

also found in the sulfation of solid CaO. Hartman and

Coughlin (1976) reported the product layer diffusivity of

6.0E-09 cm2/s at 850°C using the grain model. Georgakis et

al. (1979) applied the changing grain model and estimated

that the product layer diffusivity ranged from 8.0E-09 to

1.6E-07 cm2/s at 850°C. Ramachandran and Smith (1977)

reported the product diffusivity to be 7.5E-07 cm2/s at 850°C

using the single pore model. Christman and Edgar (1983)

reported the product diffusivity to be 4.0E-08 cm2/s at 850°C

using the distributed pore size model.

In summary, values of 10'18 < D s < 10'08 have been reported

for various noncatalytic gas-solid reactions at the

temperatures of interest. The product layer diffusivity, Ds,

will be treated as an adjustable parameter in the modeling

work which follows.

(8) Mass Transfer Coefficient

The external mass transfer coefficient can, in

principle, be estimated using the Frossling correlation

(Hughmark, 1967)

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NSh = Sherwood number, (kg) (L) / (DAB)

NRe = Reynolds number, (L) (G) / (ixa) = NSc Schmidt number, (M g ) / ( Pg ) (dab)

Dab = molecular (bulk) diffusivity, cm2/s

L = characteristic length, cm

G = mass flux of gas, g/(cm2) (min)

Mg = bulk gas viscosity, g/(cm2)(s)

Pa = bulk gas density, g/cm3. In calculating the Reynolds number, NRe, the mass flux

of gas was determined using the reactor tube diameter of 2.54

cm and the total flow rate of 500 cm3/min (STP) . At 650°C and

1 atm, the total mass flux was 0.135 g/(cm2)(min) while the

average gas viscosity was 3.8E-04 g/(cm)(sec). In the reactor

tube, the gas flowed downward and passed over the particles

which were contained in a sample pan having a diameter of

about 1 cm. If the pan diameter is considered as the

characteristic length, L, the Reynolds number (GL/jUG) is

5.92. Using Eq. (8-29) with the Schmidt number of 0.87 at

650°C and 1 atm, the Sherwood number was estimated to be 3.4,

corresponding to a mass transfer coefficient, kg, of 3.67

cm/s. If the equivalent diameter of the particle (3.1 fxm) is

taken as the characteristic length, the resultant mass

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transfer coefficient is about 1.2E+04 cm/s. In this latter

case the mass transfer resistance would be negligible under

all experimental conditions. At 650°C and 1 atm, a value of

kg = 0.5 cm/s has been used in most of the modeling effort.

In this case the mass transfer resistance is negligible at 1

atm but becomes significant at high pressure.

8.4 General Discussion of the Solution Characteristics

In this section the general characteristics of the

solution of the distributed pore size model are discussed.

The model parameters used are summarized in Table 8-3. In

order to determine the effect of intraparticle diffusion

resistance on the overall reaction, two different particle

radii are used. The initial pore size distribution as a

function of pore diameter illustrated in Figure 8.3 is also

used.

Figure 8.4 compares the conversion-time results

predicted using the distributed pore size model for two

cases. Curve A, using a particle radius of 2.5xlO'03 cm,

illustrates the results when pore diffusion resistance within

the particle is negligible. Complete conversion is predicted

after 3.5 min. The initial pore volume of the solid reactant

is 0.360 cm3/g (see Figure 8.3) which corresponds to a

porosity of 0.546. Since there is no pore diffusion

resistance within the particle, the pores fill uniformly.

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Table 8-3 Model Parameters Used for General Solution of Distributed Pore Size Model

Symbol Parameter. units Value • 4 Ro Particle Radius, cm 2.5x1 O'03 (Curve } 2.5X1002 (Curve 03

a Ratio of Molar Volumes of Product and Solid Reactant 2.2

Effective Reactive Gas Concentration, mol/cm3 1.85X10'06

Surface Reaction Rate Constant, cm/s lxlCT03

Product Layer Diffusivity, cm2/s lxlO'09

-'AB Molecular Diffusivity, cm2/s 1.00

Mass Transfer Coefficient, cm/s 10.0

Vn Molar Volume of Solid Reactant, cm3/mol 16.8

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3 0.10-

0.00 3 4 5 6 7 4 7 PORE DIAMETER, MICRONS

Figure 8.3 Cumulative Pore Volume as a Function of Pore Diameter Used for General Discussion of the Solution Characteristics

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Figure 8.4 Model Prediction of Conversion-Time Results Using Parameters in Table 8-3 and Initial Pore Size Distribution in Figure 8.3

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Further, the initial porosity is sufficiently large to allow

complete conversion to occur.

When the particle radius is increased by a factor of 10

to 2.5X10'02 cm, the pore diffusion resistance becomes

significant and the time-conversion results shown by curve B

are predicted. The reaction stops after 8 minutes as a result

of pore plugging at the outer shell of the particle, leaving

a significant amount of inaccessible unreacted solid inside

the particle. The overall conversion reached when pore

plugging occurs is 0.69.

Figure 8.5 illustrates the local porosity as a function

of radial position within the particle with the reaction time

as a parameter. Curve B parameters were used in this

calculation. Initially, the particle porosity was 0.546 at

all radial positions. After 0.5 min the local porosity at the

particle exterior surface decreased to 0.29 while the local

porosity at the center of the particle was near the original

value. The reaction stopped after 8 min when pores at the

outer shell of the particle became plugged as shown by the

zero local porosity value.

When pore diffusion resistance is negligible, the

maximum achievable conversion becomes a function only of the

initial porosity as shown in Figure 8.6. The rate of reaction

is determined by parameter values such as k, Ds, Dc, and kg.

However, given sufficient time, the conversion will always

approach the values shown in Figure 8.6. It also follows that

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t= 0 .5 min S S

—i

t= 8 min

0.00 .00 JO .60 1.00 OiMENSIONLESS RADIAL POSITION, R/RO

Figure 8.5 Local Porosity as a Function of Radial Position within the Particle with the Reaction Time as a Parameter; Significant Pore Diffusion Resistance within the Particle

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1.00

50.50

0.00 o',00 1.00 INITIAL POROSITY

Figure 8.6 Effect of Initial Particle Porosity on Maximum Achievable Conversion with Negligible Pore Diffusion Resistance; a = 2.20

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the only way in which incomplete conversion can be predicted

in a particle whose initial porosity is 0.54 or greater is by

the inclusion of significant pore diffusion resistance.

8.5 Comparison between Model Prediction and Experimental

Data

In this section the distributed pore size model

predictions are compared to experimental results using the

pore size distribution shown in Table 8-2. Run HP046 (see

Table 5-2) in which calcination was carried out at 750°C and

1 atm in N2 followed by carbonation at 650°C and 1 atm in 15%

C02/N2 has been selected for the initial or base case

comparison. Certain parameter values are selected more or

less arbitrarily to fit the experimental data for this base

case.

Thereafter, experimental runs representing the effects

of C02 mol fraction, reaction pressure, and temperature are

considered. Adjustments in the parameter values which are

consistent with theory are made and model predictions are

again compared to the experimental data.

8.5.1 Base Case Comparison

Figure 8.7 compares three cases of model predictions

with the experimental results from the base run. Table 8-4

summarizes the values of the model parameters which were

fixed at the beginning and were not varied thereafter.

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Table 8-4 Model Parameters Whose Values Were Not Changed in Modeling Test HP046

Svmbol Parameter Value

Ro Particle Radius, cm 1.55x10 a Ratio of Molar Volumes of Product and Reactant, 2.20 y C02 Mol Fraction 0.15 f Tortuosity Factor 3.0 p Mass Density of CaO, g/cm3 3.345 k Reaction Rate Constant, cm/s 3.54x10 kg Mass Transfer o in

Coefficient, cm/s • T Reaction Temperature, C 650 P Total Pressure, atm 1

P c , C02 Equilibrium Pressure, atm 0.01

Table 8-5 Model Parameters Whose Values Were Adjusted in Modeling Test HP046

Case D „ . cm2/s D . . a , cm2/s

A 2. 2xl0'14 1.4X10’02

B 1. 7x1 O'09 1.4X10'02

C 1.7X10'09 1. 3X10'06

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Sorbent 1 (HP046) Calcination: 750C, N 2,1 atm Carbonation: 650C, 15SC02/N2,1 atm

Figure 8.7 Comparison between Model Predictions and Experimental Data of Run HP046

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Parameter values which were varied in the three model cases

are shown in Table 8-5.

Curve A in Figure 8.7 represents the model prediction

using Case A. After 6 minutes the predicted overall

conversion was only 0.05 while the experimental overall

conversion was about 0.70 after 1 minute. The product layer

diffusion resistance associated with Ds = 2.2xl0'14 cm2/s was

the dominant resistance. Although the rate of reaction is

quite small, pores fill uniformly and complete reaction would

be predicted if the reaction time was sufficiently large.

Increasing the value of Ds to 1.7X10’09 cm2/s while the

other parameters were unchanged (Case B) produced the time-

conversion result shown by curve B. The model predicted

complete carbonation in approximately 2 minutes. Both surface

reaction and product layer diffusion resistances were

important. Since the pore diffusion resistance within the

particle was negligible and the initial solid porosity was

0.548, all pores were filled uniformly and complete

carbonation was predicted.

The only way to predict incomplete conversion with e0 =

0.548 is to force pore diffusion resistance within the

particle to become important. Curve C shows the effect of

decreasing the initial effective diffusivity to 1.3X10'06

cm2/s. This unreasonably small value of Dc0 produced

significant pore diffusion resistance and caused the reaction

to stop after 2.5 minutes due to pore plugging at the outer

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shell of the particle, leaving inaccessible pores inside the

particle. The final overall fractional carbonation predicted

was 0.726 compared to the experimental value of 0.70. The

agreement between model and experiment was quite good

throughout.

8.5.2 Effect of C02 Mol Fraction at Constant Temperature

and Pressure

The effect of C02 mol fraction was examined using the

experimental data of run HP043 (Table 5-2). Calcination was

at 750°C and 1 atm in N2 followed by carbonation at 650 and

1 atm in 5% C02/N2. The only parameter to change was the C02

mol fraction; other parameter values were the same as shown

in Tables 8-4 and 8-5, Case C. Figure 8-8 compares the model

prediction to the experimental data. Good agreement between

model and experiment was achieved for the first two minutes.

Thereafter, the predicted conversion was slightly less than

the experimental. According to the model, pore plugging at

the particle exterior would occur after 9 minutes with an

overall fractional conversion of 0.726. The experimental

fractional conversion after 9 minutes was 0.732.

8.5.3 Effect of Pressure with Constant C02 Concentration

The experimental data for run HP137 (Table 5-2), with

calcination at 750°C and 1 atm in N2 and carbonation at 15

atm and 650°C in 1% C02/N2, was selected to evaluate the

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Sorbent 1 (HP043) Calclnotton: 750C, N 2 ,1 atm Carbonation: 650C, 5XC02/N2,1 atm

0.00 f i i i i i i " " i ■ » 0 5 10 TIME. MIN.

Figure 8.8 Comparison between Model Prediction and the Experimental Data of Run HP043; Effect of C02 Mol Fraction

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effect of pressure. Bulk C02 concentration for this run using

1% C02 at 15 atm was the same as the base case run using 15%

C02 at 1 atm. The values of Ds and k were maintained at 1.7x10'

09 cm2/s and 3.54X10'03 cm/s, respectively, since the reaction

temperature did not change. The effect of pressure on the

effective diffusivity was negligible because the value of Dt0

= 1.3X10'06 cm2/s was within the region where Knudsen diffusion

would dominate. Figure 8.9 compares the model predictions

with experimental data using two different values of mass

transfer coefficient, kg. The value of kg = 0.033 cm/s

(0.5/15) was selected because kg should be approximately

inversely proportional to the reaction pressure. With kg =

0.033 cm2/s, the ratio of the initial particle surface

concentration to the effective bulk C02 concentration

(C(R=R0)/C0) was 0.31, indicating that mass transfer provided

the most important resistance initially. However, as the

reaction progressed and pore plugging was approached the pore

diffusion resistance began to dominate. As seen in the

figure, the predicted overall conversion was significantly

larger than the experimental result during the early portions

of the run. Pore closure was predicted after 8 minutes at a

fractional conversion of 0.726 compared to the experimental

value of 0.68 at that time. Decreasing the value of kg to

0.01 cm/s increased the importance of the mass transfer

resistance, and decreased the ratio of initial surface

concentration to the effective bulk C02 concentration to

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sorbont 1 (HP137) Caldnotiofi: 750C, N 2,1 atm Carbonation: 650C, 1ZC02/N2,15 atm

0.004 0 5 10 15 20 TIME, MIN.

Figure 8.9 Comparison between Model Prediction and Experimental Data of Run HP137; Effect of Carbonation Pressure

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 233

0.12. With this value of kg the agreement between prediction

and experiment improved significantly as shown in Figure 8.9.

Pore closure was predicted after 2 0 minutes when the overall

conversion was 0.726. The experimental conversion after 20

minutes was 0.70.

8.5.4 Effect of Temperature

Carbonation temperature should affect the model

parameter values k, Ds, Dc, kg/ and C0. The intrinsic reaction

rate constant, k, is expected to increase with temperature

according to the Arrhenius relationship. However, Bhatia and

Perlmutter (1983) reported an activation energy of zero for

the intrinsic rate constant. The product layer diffusivity,

Ds, is expected to be strongly temperature dependent. The

temperature relationship should also be given by the

Arrhenius equation with a large activation energy. The value

of the effective diffusivity, De, should increase slightly

since De is controlled by Knudsen diffusion which is

proportional to T*. The mass transfer coefficient kg should

also increase slightly with temperature. The effective bulk

C02 concentration, C0, decreases with increasing temperature

while the equilibrium C02 pressure increases with

temperature.

Figure 8.10 compares three model predictions with the

experimental data for run HP066 (Table 5-2) . Calcination was

carried out at 750°C and 1 atm in N2, and carbonation was at

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 234

1.0*

Sorbtnf 1 (HP066) CdcM oiu 750C, N 2,1 atm Carbonation: 750C, 15SC02/N2,1 atm

5 10 15 TIME* MIN.

Figure 8.10 Comparison between Model Predictions and Experimental Data for Run HP066; Carbonation at 750°C and 1 atm in 15% C02/N2

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Table 8-6 Model Parameters Used for Carbonation Reaction for Run HP066

Symbol Parameter, units Value

T Reaction Temperature, °C 750

«1 C02 Equilibrium Pressure, atm 0.082 Mass Transfer Coefficient, cm/s 0.53

-'cO Initial Effective Diffusivity, cm2/s 1.4X1006

Reaction Rate Constant, cm/s Curve A: 6.0xl0°3 (Ea = 10 kcal/mol) Curve B: 3.54xlO'03 (Ea = 0 kcal/mol) Curve C: 3.54xl0'03 (Ea = 0 kcal/mol)

D. Product Layer Diffusivity, cm2/s Curve A: 1.6xl0'08 (Ea = 42 kcal/mol) Curve B: 5.2X10'09 (Ea = 21 kcal/mol) Curve C: 1.7X10'09 (Ea = 0 kcal/mol)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 236

750°C and 1 atm in 15% C02/N2. Table 8-6 summarizes the model

parameters used for the three model predictions. Three values

of reaction rate constant, k, and product layer diffusivity,

Ds, were calculated based upon the activation energies shown

in the table. Curve A represents the values k and Ds, using

the highest activation energies of 10 and 42 kcal/mol,

respectively, while curve B represents the values of zero

activation energy for the reaction rate constant and 21

kcal/mol for the product layer diffusivity. Zero activation

energies for both k and Da were assumed in curve C. As seen

in Figure 8.10, none of the predicted conversion-time results

were in good agreement with the experimental results during

the rapid reaction phase. For curve A, pore plugging was

predicted after about 1.5 min with an overall conversion of

0.45. For curve B, pore plugging was predicted after 3 min

with an overall conversion of 0.60. For curve C, using zero

activation energies for both k and Ds, pore plugging was

predicted after 6 min with an overall conversion of 0.77,

compared to the experimental conversion of 0.75 at that time.

A similar approach was used to compare the model

prediction to the experimental data at the lower carbonation

temperature of 550°C. Figure 8.11 compares the model

predictions to the experimental data for run HP049 (Table 5-

2) . Calcination was at 750°C and 1 atm in N2, and carbonation

was at 550°C and l atm in 15% C02/N2. Table 8-7 summarizes the

model parameters used for the three model predictions. Curve

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 237

Table 8-7 Model Parameters Used for Carbonation Reaction for Run HP049

Symbol Parameter, units Value

T Reaction Temperature, °C 550

■ «i C02 Equilibrium Pressure, atm 0.0007 Mass Transfer Coefficient, cm/s 0.47

Jc0 Initial Effective Diffusivity, cm2/s 1.23X10'06

Reaction Rate Constant, cm/s Curve A: 1.82X10'03 (Ea = 10 kcal/mol) Curve B: 3.54xl0'03 (Ea = 0 kcal/mol) Curve C: 3.54xl0'°3 (Ea = 0 kcal/mol)

Product Layer Diffusivity, cm2/s Curve A: 1.05xl0‘10 (Ea = 42 kcal/mol) Curve B: 4.2xlO‘10 (Ea = 21 kcal/mol) Curve C: 1 .7X1009 (Ea = 0 kcal/mol)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 238

1.0fr

Sorbont 1 (HP049) Calcination: 750C, N 2 ,1 atm Carbonation: 5S0C, 15X C 02/N 2,1 atm

O.OOh 0 2 4 6 TIME, MIN.

Figure 8.11 Comparison between Model Predictions and Experimental Data for Run HP049; Carbonation at 550°C and l atm in 15% C02/N2

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 239

A, using the highest activation energies to calculate k and

Ds, shows the predicted rate to be slower than the

experimental result during early stages of the reaction.

However, complete conversion after 16 minutes (not shown) was

predicted, in contrast with the experimental data where the

final conversion was 0.67 after 55 minutes. When the lower

activation energy for product layer diffusivity (21 kcal/mol)

and zero activation energy for the reaction rate constant

were used (curve B) , improved agreement during the early

reaction phase was achieved, but complete conversion was

predicted after 8 minutes (not shown). Curve C, in which zero

activation energies were used to calculate k and Ds provided

reasonable agreement throughout the reaction. Pore plugging

was predicted after 2.3 min with an overall conversion of

0.72, compared to an experimental conversion of 0.64 at that

time.

Figure 8.12 compares predicted maximum conversions from

Figures 8.10 and 8.11 with the experimental "maximum"

conversion at the three carbonation temperatures. The

experimental "maximum" increased with temperature while the

predicted maximum decreased with temperature except when zero

activation energies were used for both reaction rate constant

and product layer diffusivity.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 240

1.00

(HP066) (HKUsifx' - (HP049)

0.00 500 600 700 800 CARBONATION TEMPERATURE, C

Figure 8.12 Comparison between Predicted Maximum Conversions and Experimental "Maximum" Conversion at Different Carbonation Temperatures

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8.6 Model Predictions with No Pore Diffusion Resistance

Using a Modified Pore Size Distribution

As discussed previously, the model predicts complete

carbonation given sufficient time when the initial porosity

is equal to or greater than 0.54 and when pore diffusion

resistance is negligible. In the previous section, incomplete

conversion due to pore plugging was achieved by arbitrarily

reducing De0 to a value several orders of magnitude than

expected.

Mercury porosimetry results for calcined CaO from Table

8-2 (Narcida, 1992) showed that the pore volume was primarily

associated with pore diameters in the 0.026 - 0.08 jum range,

with additional pore volume contributed by pore diameters <

0.01 jtim. The surface area of the calcined CaO reported by the

mercury porosimeter, including the smallest pores with <0.01

Atm diameter was 99 m2/g, well above the measured BET surface

area of 18.5 m2/g (Narcida, 1992). However, if the smaller

pores in the < 0.026 jum diameter range are ignored, the

mercury porosimeter surface area was 22.7 m2/g, reasonably

close to the measured BET surface area.

The reliability of mercury porosimeter results at the

high pressure range corresponding to pore diameters less than

0.01 /zm is suspect. Sample compression and instrument blank

error are known to occur at the highest porosimeter pressures

(Micromeritics, 1990). By ignoring the pores in the 0.003 -

0.026 jum diameter range in Table 8-2, the initial pore volume

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of CaO is reduced to 0.26 cm3/g, corresponding to an initial

porosity of 0.47. The theoretical maximum conversion is,

therefore, limited to 0.74 which is close to the

experimentally determined maximum conversion. This modified

pore size distribution has been used the following modeling

cases.

8.6.1 Base Case Comparison

Figure 8.13 compares the model prediction with the

experimental results from the base run (HP046) . The model

parameters shown in Table 8-4 were used with the exception of

the reaction rate constant, k. DAB was estimated from Eq.(8-

25) to be 1.08 cm2/s giving the initial effective

diffusivity, Dc0, of 1.6xlO°2 cm2/s. The values of k and Ds were

2xlO'03 cm/s and 2X10'09 cm2/s, respectively, chosen to match the

experimental data. As seen in Figure 8.13, the predicted

conversion-time matched the experimental data quite well

during the rapid reaction phase. Both surface reaction and

product layer diffusion resistances were important. Due to

the fact that pore diffusion resistance within the particle

was negligible, the pores filled uniformly leading to the

predicted maximum conversion was 0.74 which would be reached

in about 2 minutes. At that time the experimental conversion

was 0.69. The actual reaction continued at a slow rate and

the conversion increased to 0.73 after 40 minutes.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 243

1.0ft

Sorbent 1 (HP046) ta. Calcination: 750C, N 2 ,1 atm Carbonation: 650C, 15ZC02/N2,1 atm

0.00 0 2 4 6 TIME, MIN.

Figure 8.13 Comparison between Model Prediction and Experimental Data of Run HP046 Using Modified Pore Size Distribution

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 244

8.6.2 Effect of C02 Mol Fraction at Constant Temperature

and Pressure

Figure 8.14 compares the model prediction with the

experimental data from run HP043 in which the C02 mol

fraction was reduced to 0.05 at constant carbonation

temperature and pressure. The only model parameter to change

was the C02 mol fraction; other parameter values were the

same as shown in Table 8-4 coupled with the values of k, De0/

and Ds used in the previous section. Good agreement between

the model and the experiment was achieved for both rapid

reaction and slow reaction phases. The predicted pore filling

occurred after about 8 minutes. The experimental conversion

of 0.73 at 8 minutes was effectively identical to the value

of 0.74 predicted by the model.

8.6.3 Effect of Pressure with Constant C02 Concentration

Figure 8.15 compares the experimental data of run HP137

with model predictions using three different values of kg.

Calcination was at 750°C and 1 atm in N2 and carbonation at

650°C and 15 atm in 1% C02/N2. The C02 concentration at these

conditions was the same the base run using 15% C02 and 1 atm

(HP046) . The value of DAB was reduced to 0.072 cm2/s

(1.08/15) according to Eq. (8-25) which produced a value of Dc0

= 6.7xl0'03 cm2/s. Three values of kg were used in order to

match the experimental data. The other model parameters were

the same as previously used.

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1.00

Sorbent 1 (HP043) Calcination: 750C, N 2 ,1 atm Carbonation: 650C, 5XC02/N2,1 atm

Figure 8.14 Comparison between Model Prediction and the Experimental Data of Run HP043; Effect of C02 Mol Fraction/ Using Modified Pore Size Distribution

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 246

1.0*

kg = 0.033 em/s

0.01 0.004

Sorbsnt 1 (HP137) Calcination: 750C, N 2,1 dm Carbonation: 650C, 1XC02/N2,15 d r

0.0* 0 5 10 15 20 TIME. MIN.

Figure 8.15 Comparison between Model Prediction and Experimental Data of Run HP137; Effect of Carbonation Pressure, Using Modified Pore Size Distribution

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 247

As seen in Figure 8.15, the kg values of 0.03 3 and 0.01

cm/s used in the previous modeling resulted in a significant

difference between the model and experiment during the rapid

reaction phase. However, if kg = 0.004 cm/s was used, quite

good agreement between experiment and prediction was

achieved. The ratio of initial C02 concentration at the

particle surface to the effective bulk C02 concentration was

0.10, very close to the value of 0.12 associated with kg =

0.01 cm/s used in the previous section.

8.6.4 Effect of Temperature

The effect of carbonation temperature was examined, as

before, using runs HP066 (750°C) and HP049 (550°C). Since

pore diffusion resistance was negligible, the theoretical

maximum conversion of 0.74 was always achieved given

sufficient time regardless the carbonation temperature was

used.

Figure 8.16 compares the experimental data to the

model predictions using three cases of k and Ds for run

HP066, in which carbonation was at 750°C and 1 atm in 15%

C02/N2. The model parameters, summarized in Table 8.8, were

based upon the same values of activation energy for k and Ds

as used in the previous section. For all three cases, the

model predicted a faster rate during the early reaction phase

than measured experimentally. Curve A, whose k and Ds values

were based upon the highest activation energies, exhibited

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Table 8-8 Model Parameters Used for Carbonation Reaction for Run HP066 Using Modified Pore Size Distribution

Symbol Parameter, units Value

T Temperature, °C 750

Pcq C02 Equilibrium Pressure, atm 0.082

ks Mass Transfer Coefficient, cm/s 0.53

D ab Bulk Diffusivity, cm2/s 1.26

Dco Initial Effective Diffusivity, cm2/s 1.7xl0'02

Reaction Rate Constant, cm/s Curve A : 3. 4xl0'03 (Ea = 10 kcal/mol) Curve B : 2 . OxlO'03 (Ea = 0 kcal/mol) Curve C : 2. 0X1 O’03 (Ea = 0 kcal/mol)

Product Layer Diffusivity, cm2/s Curve A : 2. lxlO'08 (Ea = 42 kcal/mol) Curve B : 6.1X1 O’09 (Ea = 21 kcal/mol) Curve C : 2. OxlO'09 (Ea = 0 kcal/mol)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sorbent 1 (HP066) Calcination: 750C, N 2 ,1 atm Carbonation: 7S0C, 15ZC02/N2,1 atm

0.00 I mTm 5 10 IS TIME, MIN.

Figure 8.16 Comparison between Model Predictions and Experimental Data for Run HP066; Carbonation at 750°C and 1 atm in 15% C02/N2, Using Modified Pore Size Distribution

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 250

the highest initial reaction rate. The maximum conversion of

0.74 associated with complete pore filling was predicted

after 1.7 min; the experimental conversion at that time was

only 0.4. The maximum conversion from curve B, using zero

activation energy for k and an activation energy of 21

kcal/mol for Ds, was predicted after 3 min. The experimental

conversion at that time was 0.6. When zero activation

energies for both k and Ds were applied, the result is shown

in curve C. The theoretical maximum conversion was predicted

after 5 minutes, and the experimental conversion at that time

was also 0.74.

Comparison between the model predictions and the

experimental data for run HP049 using a carbonation

temperature of 550°C is shown in Figure 8.17. The model

parameters used are summarized in Table 8.9. Curve A, using

the highest activation energies to calculate k and Ds values,

shows a significantly slower rate than measured

experimentally during the early portions of reaction. The

maximum conversion of 0.74 was predicted after 19 minutes

(not shown) compared to the experimental conversion of 0.66

at that time. Curve B, using zero and 21 kcal/mol activation

energies to calculate k and Ds, respectively, predict

complete pore filling associated with the maximum conversion

of 0.74 after 5 minutes compared to the experimental

conversion of 0.65 at that time. Curve C, in which zero

activation energies were used to calculate k and Ds, was in

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Table 8-9 Model Parameters Used for Carbonation Reaction for Run HP049 Using Modified Pore Size Distribution

Symbol Parameter, units Value

T Temperature, °C 550

Pcq C02 Equilibrium Pressure, atm 0.0007

K Mass Transfer Coefficient, cm/s 0.47

Dab Bulk Diffusivity, cm2/s 0.91

De0 Initial Effective Diffusivity, cm2/s 1.5X10'02

Reaction Rate Constant, cm/s Curve A : l.OxlO'03 (Ea = 10 kcal/mol) Curve B : 2. OxlO'03 (Ea = 0 kcal/mol) Curve C : 2. OxlO'03

D. Product Layer Diffusivity, cm2/s Curve A : l.24xlO'10 (Ea = 42 kcal/mol) Curve B : 5,OOxlO'10 (Ea = 21 kcal/mol) Curve C : 2 . OxlO'09 (Ea = 0 kcal/mol)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 252

1.00

SortMftt 1 (HP049) Calcination: 750C, N 2 ,1 otm Carbonation: 550C, 15JC02/N2,1 atm

TIME, MIN.

Figure 8.17 Comparison between Model Predictions and Experimental Data for Run HP049; Carbonation at 550°C and 1 atm in 15% C02/N2, Using Modified Pore Size Distribution

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 253

reasonably good agreement with the experiment during the

early reaction phase. The maximum conversion of 0.74 was

predicted after about 2 minutes, compared to the experimental

conversion of 0.64 at that time.

8.7 Summary

The distributed pore size model has been used to

describe the experimental data for the carbonation reaction

of sorbent 1. This sorbent was chosen because of its well

defined structural properties and noticeably incomplete

conversion during the reaction.

The initial pore size distribution of calcined CaO

reported by Narcida (1992) produced an initial porosity of

0.548. The pore volume was primarily associated with pore

diameters of 0.02 - 0.08 fim with a small additional pore

volume in the < 0.01 /xm diameter range.

The model parameters were first estimated using

literature values, diffusion theory, and literature

correlations. With this approach, it was found that pore

diffusion resistance within the particle was negligible. As

a result, based upon the initial porosity of 0.548, complete

carbonation was always predicted given sufficient time. The

only way to predict incomplete conversion was to force the

pore diffusion resistance to become important by using a very

small value of the initial effective diffusivity, D c0.

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Incomplete conversion was predicted using the "new"

and "reasonable" model parameters were found which resulted

in good agreement between model and experiment for a base run

in which carbonation was carried out at 650°C and 1 atm in

15% C02/N2. When these model parameters were used to examine

the effect of C02 mol fraction at constant temperature and

pressure, the agreement between the model and experiment was

quite good. Qualitative agreement between the model and

experiment was also found when the effect of pressure at

constant temperature and C02 concentration was modelled using

a "best-fit" mass transfer coefficient. The effect of

carbonation temperature was modelled reasonably well when

both intrinsic rate constant and product diffusion

coefficient were taken to be independent of temperature.

An alternative approach in which the initial pore size

distribution was modified by neglecting pore volume

associated with pore diameters less than 0.026 /xm was also

used to model the data. The initial porosity of the CaO was

reduced to 0.47. Based on this value, the theoretical maximum

conversion of 0.74 was close to the experimentally determined

maximum conversion. This maximum conversion was associated

with uniform filling of the pores along their length and was

achieved when pore diffusion resistance was negligible. The

modification of the initial pore size distribution was

justified on the basis of sample compression and instrument

blank error which occur at the highest porosimeter pressures.

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The model predictions using the modified pore size

distribution showed good agreement with the experimental

results of the base case. "Best-fit" values of k and Ds were

practically the same as those using the original pore size

distribution. Also good agreement between prediction and

experiment was found in examining the effect of C02 mol

fraction at constant temperature and pressure. Using the

"best-fit" mass transfer coefficient, kg, agreement was also

obtained between model experiment when the carbonation

pressure was increased. In order to model the effect of

carbonation temperature, it was again necessary to assign

zero activation energies to the intrinsic rate constant and

product layer diffusion coefficient.

In summary, neither approach was completely satisfactory

in modeling the experimental results. Good agreement between

the model prediction and experiment was achieved for runs at

650°C. However, the absence of a strong temperature effect

could only be matched by assigning zero activation energies

to k and Ds, both of which should have quite large activation

energies.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 9

Conclusions and Recommendations

for Future Work

Advantages associated with the high temperature removal

of C02 from coal gas before further processing include

increased heating value of the fuel gas, increased efficiency

of the shift conversion process for production of hydrogen or

methanol and ammonia synthesis gas, and improved efficiency

of molten carbonate fuel cells.

A potential application of particular interest is a

combination of the water-gas shift reaction with C02 removal

in one reactor, thereby providing for the direct production

of hydrogen in a single-step process. Such a process would be

much simpler and potentially less expensive than the current

multi-step catalytic processes for hydrogen production.

The removal of C02 using regenerable calcium-based

sorbents at high temperature and high pressure has been

investigated in this study. C02 removal is based upon the

noncatalytic gas-solid reaction between C02 from the coal gas

and CaO-based sorbents to produce CaC03 according to

C a 0 (.s) + C 0 2(g) ~ C a C 0 H s )

The forward (carbonation) reaction is favored by high

pressure and is feasible in the temperature range of 550-

750°C. Approximately 99.6% C02 removal from a coal gas

256

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containing 15%(vol) C02 at 15 atm and 650°C is theoretically

possible. Accordingly, the reverse (calcination) reaction is

favored by lower pressure, higher temperature, and/or lower

C02 pressure.

A high-pressure thermobalance reactor was used to study

the kinetics of the calcination and carbonation reactions as

a function of temperature, pressure, C02 concentration, and

background gas composition. A number of CaO-based sorbent

precursors were studied and multicycle calcination and

carbonation runs were carried out in order to have a better

understanding of sorbent durability, a very important

property in a commercial process.

Three out of nine sorbent precursors were selected for

detailed kinetic studies. They were (i) reagent grade calcium

carbonate (sorbent 1) considered as the standard or reference

sorbent, (ii) reagent grade calcium acetate (sorbent 7), and

(iii) commercial grade dolomite (sorbent 9) having

essentially equimolar quantities of MgC03 and CaC03. The three

sorbent precursors produced a wide range of structural

properties following calcination (Narcida, 1992).

In particular, calcination of the three sorbents

produced different pore volumes and pore size distributions.

In sorbent 7, the pore volume was created first by driving

off the water of hydration, then decomposing the calcium

acetate to calcium carbonate, and finally decomposing calcium

carbonate to calcium oxide. The pore volume in sorbent 9 was

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created by decomposing both MgC03 and CaC03. Since MgO, at the

carbonation conditions of interest, was inert, "excess" pore

volume created by MgC03 decomposition allowed the complete

carbonation of CaO. The pore volume in sorbent 1, on the

other hand, was created only by decomposing CaC03; therefore,

no "excess" pore volume was available.

Carbonation of sorbent 1 was characterized by an initial

rapid reaction followed by an abrupt transition to a slow

reaction well before complete carbonation. The maximum

fractional conversion which could be achieved was only about

0.75. In contrast, almost complete carbonation of CaO to

CaC03 was possible using both sorbents 7 and 9. These

reactivity differences may be attributed directly to the

different structural properties of the calcined sorbents.

Two-cycle calcination-carbonation kinetics of the three

sorbent precursors as a function of temperature, pressure,

and C02 mol fraction in N2 were investigated. Calcination

temperatures of 750, 825, and 900°C, carbonation temperatures

of 550, 650, and 750°C, calcination pressure of 1 atm,

carbonation pressures of 1, 5, and 15 atm, and C02 mol

fractions of 0.01, 0.05, and 0.15 were used. Reactivity and

capacity indices were defined in order to permit direct

comparison of the experimental results. The following

conclusions were reached:

(1) Calcination at 900°C produced a significant adverse

effect on carbonation performance for all three sorbents, in

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particular, the second-cycle carbonation performance

deteriorated due to sintering at the high calcination

temperature. Calcination at 750°C resulted in better

carbonation capacity maintenance for all sorbents.

(2) Carbonation at 650 to 750°C was found to be

favorable in term of reactivity, capacity, and capacity

maintenance. Carbonation at 550°C unexpectedly showed a

significant drop in capacity maintenance compared to the

higher temperatures. This adverse behavior may be due to the

different structure of the product carbonate formed at high

and low temperature (Bhatia and Perlmutter, 1983; Mess,

1989).

(3) Sorbent reactivity decreased with increasing

carbonation pressure. Transport resistances were important in

establishing reactivity, particularly at high pressure.

Carbonation pressure had little effect on sorbent capacity in

either cycle, or on capacity maintenance.

(4) C02 mol fraction had an effect only on reactivity.

As expected, the reactivity increased with increasing C02 mol

fraction. Sorbent capacity, on the other hand, was

independent of C02 mol fraction.

(5) Sorbents 7 and 9 had a clear advantage over sorbent

1 in terms of both capacity and capacity maintenance.

Sorbents 7 and 9 were somewhat more reactive in both cycles

than sorbent 1. There were no significant reactivity

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differences between sorbents 7 and 9, although the reactivity

maintenance of sorbent 7 was slightly higher than sorbent 9.

The experimental study was then extended to multicycle

runs in which the effects of calcination pressure,

carbonation temperature, and background gas composition were

investigated using the three sorbent precursors. The

following conclusions were reached:

(1) Sorbent 1 exhibited the lowest reactivity

maintenance and capacity maintenance after being subjected to

five-cycle runs. Sorbent 7 had the highest calcium

utilization in the first cycle, but experienced a gradual

decrease in capacity with increasing number of cycles.

Sorbent 9 was the best sorbent in terms of reactivity

maintenance and capacity maintenance.

(2) Calcination at 15 atm was feasible at a temperature

of 750°C. Moreover, reactivity, capacity, and capacity

maintenance for the subsequent carbonation reaction showed no

adverse effect of high calcination pressure.

(3) The addition of H20, CO, and H2 to simulate a sulfur-

free coal-gas resulted in improved sorbent reactivity,

capacity, and durability. Importantly, the increase in

carbonation reactivity was consistent with a higher

concentration of C02 formed by the water-gas shift reaction.

(4) The addition of H2S to the simulated coal gas caused

a rapid and irreversible deterioration in carbonation

capacity because of the irreversible CaO + H2S reaction to

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form CaS. In addition, H2S was capable of displacing

previously formed carbonate (CaC03) to form CaS. A prior

desulfurization step would be required before the regenerable

calcium-based sorbent process could be used commercially for

C02 removal. Simultaneous C02 - H2S removal could be carried

out if the sorbent was used on a once-through basis or for a

small number of cycles.

A few ten-cycle runs using sorbents 7 and 9 were also

carried out. Sorbent 7 suffered a small capacity loss in each

cycle with the capacity decrease over ten cycles less than

10%. Sorbent 9 possessed superior durability. The capacity in

the tenth cycle was only about 3% lower than in the first

cycle.

The distributed pore size distribution model developed

by Christman and Edgar (1983) was chosen to model the

carbonation reaction for sorbent 1. The initial pore size

distribution reported by Narcida (1992) was used. When a

priori best estimates of the model parameters were used,

complete conversion was predicted given sufficient time since

pore diffusion resistance within the particle was negligible.

By forcing the initial effective diffusivity, De0, to a very

small value (i.e. forcing pore diffusion resistance to become

important), pore plugging was predicted at the outer surface,

leaving inaccessible unreacted solid inside the particle.

Using this approach, good agreement between the model and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 262

experiment was achieved for runs at 650°C and varying

pressure and C02 concentration.

The pore size distribution was then modified by

neglecting pores whose diameters were less than 0.026 jum and

the modeling was repeated. This reduced the initial porosity

of the sorbent from 0.548 to 0.47, which limited the maximum

fractional conversion to 0.74. With a negligible pore

diffusion resistance, this maximum fractional conversion,

which was always predicted, was in reasonably good agreement

with the experimental data.

Neither approach was completely satisfactory when the

model was applied at different carbonation temperatures. The

absence of strong temperature effect, which was observed

experimentally, could only be matched by assigning zero

activation energies to the intrinsic rate constant and the

product layer diffusion coefficient, both of which should

have quite large activation energies.

Based on the above conclusions, the following

recommendations for future work are offered.

(1) One of interesting results from this study was the

indirect evidence of the simultaneous water-gas shift

reaction and C02 removal taking place at high temperature.

This should be confirmed by performing studies using a small

fixed-bed reactor having capability for inlet and outlet gas

analysis. Simultaneous occurrence of the two reactions could

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 263

provide an alternate method for H2 synthesis in which H2 could

be produced at high temperature in a simple one-step process.

(2) Dolomite with equimolar quantities of MgC03 and CaC03

showed superior carbonation capacity maintenance after

multicycle runs. However, MgO present in the sorbent lowered

the C02 capacity per gram of sorbent. Studies on the effect

of MgO concentration would be beneficial in a number of

areas. Reducing the MgO content would be desirable from the

capacity standpoint but less "excess" pore volume would be

created. Another important question is whether the sole

function of MgC03 is simply to create excess pore volume or

does it also stabilize the sorbent for multicycle runs. In

addition, this work would be help to answer the question of

whether MgO serves as a catalyst for the water-gas shift

reaction.

(3) One particular dolomite from National Lime, Co.,

Findley, Ohio, was used in this study. Since dolomites having

different properties are available throughout the country, a

screening study should be conducted to determine if favorable

reaction characteristics are a general property of all

dolomites, or if careful selection of particular dolomites

will be required.

(4) A preliminary design study and economic analysis

should be conducted to determine the commercial potential of

hydrogen production via the simultaneous water-gas shift

reaction and C02 separation at high temperature and high

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 264

pressure. Results should be compared to a conventional

hydrogen production process using two stages of water-gas

shift reactors with either pressure swing adsorption or C02

scrubbing for hydrogen purification.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. References

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nomenclature

Cb bulk reactive gas concentration, mol/cm3

equilibrium reactive gas concentration, mol/cm3

C0 effective gas concentration, mol/cm3

c(r2) gas concentration at the reaction interface, mol/cm3

Dab bulk diffusivity of gas mixture, cm2/s

Dc combined bulk and Knudsen diffusivity, cm2/s

De effective diffusivity, cm2/s

Dk Knudsen diffusivity, cm2/s

Ds product layer diffusivity, cm2/s

Ea activation energy, kcal/mol

k surface reaction rate constant, cm/s

Ka overall equilibrium for combined reactions as defined in Eq.(l-5)

Ke effective reactivity, 1/s

kg mass transfer coefficient, cm/s

Kpi equilibrium constant for reaction i

1 cylindrical pore length between R and (R+dR), cm

Ma molecular weight of species A, g/gmol

p total pressure, atm

Pi partial pressure of component i, atm

p^ equilibrium pressure of reractive gas, atm

r0 initial pore radius, cm

rt pore radius, cm

r2 radius of product-reactant interface, cm

272

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R radial position of in particle, cm

Rq initial radius of particle, cm

T temperature, K

t time, s

v a / v b molar volumes of solid reactant A and solid product B, cm3/mol

Yi mol fraction of reactive gas i

a ratio of molar volume of solid product and solid reactant

j8; stoichiometric coefficient of component i

5, distance between the original pore wall (at time = 0) and the current pore wall (at time = t) in the Single Pore Model

S2 distance between the original pore wall (at time = 0) and the current reaction interface in the Single Pore Model

e porosity of porous matrix

e0 initial porosity of solid reactant

f tortuosity

X dimensionless constant defined in Eq.(8-10)

ij, number of pores intersecting a unit area per unit radius (r,) of cylindrical pore

pQ bulk gas viscosity, g/cm2.s

p mass density of solid reactant, g/cm3

pG bulk gas density, g/cm3

ctab Lennard-Jones parameter, A

t cummulative gas concentration defined in Eq.(8-7), s

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\p void area per unit area defined in Eq. (8-13)

n D,AB dimensionless function of temperature and of the intermolecular potential field for one molecule of A and one of B

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix A

Master List of Runs

Initial Calcination Carbonation Number R u n S o rb e n t W e ig h t o f (m g ) T e m p . G as Press. T e m p . G as Press. C y c le ( ° C ) (a tm ) CQ (atm )

H P 1 4 6 9 1 2 .5 7 7 50 N 1 750 A 1 5

H P 1 4 7 7 12.66 7 5 0 N 1 6 5 0 A 1 5

H P 1 4 8 1 11.29 750 N 1 750 A 1 5

H P I4 9 7 12.36 7 5 0 N 1 7 5 0 A 1 5

H P 1 5 0 CMA 1 9 .4 4 7 50 N 1 750 A 1 2

H P 151 C M A 12 .5 0 7 5 0 N 1 750 A 1 5

H P 1 5 2 C M A 12.54 7 50 N 1 750 A 1 2

H P 153 9 12.67 750 N 15 750 A 15 5

H P 1S 4 9 12 .4 2 7 5 0 N 15 65 0 A 15 5

H P 1 5 5 7 12 .9 0 7 5 0 N 15 650 A 15 5

H P 1 5 6 7 12.35 7 5 0 N 15 750 A 15 5

H P 1 5 7 7 12.32 750 N 1 650 A 15 5

H P I5 8 7 12.48 750 N 1 750 B 1 2

H P 1 5 9 7 12.38 7 5 0 N 1 750 B 1 2

H P 161 9 12.63 750 N 1 750 A 15 5

H P 1 6 2 7 12.53 7 5 0 N 1 7 5 0 A 15 5

H P 163 9 12.72 750 N 1 650 A 15 5

H P 1 6 8 9 12.71 7 5 0 N 1 7 50 A 1 5

H P 1 6 9 9 12 .8 7 7 5 0 N 1 7 5 0 A 1 2

H P 1 7 0 9 12.75 75 0 N 1 7 50 B 1 5

H P 1 7 2 9 12.72 7 5 0 N 1 650 A 1 2

H P 1 9 9 7 12.68 6 5 0 N 1 650 A 15 2

H P 2 0 0 7 12.16 7 5 0 N 750 A 15 2

H P 2 0 5 9 12.53 750 N 15 7 50 B 15 5

H P 2 0 6 7 12 .6 4 7 5 0 N 15 750 B 15 5

H P 2 0 7 9 12 .2 0 7 5 0 N 7 5 0 B 15 5

H P 2 0 8 9 12.60 750 N 15 6 50 B 15 5

H P 2 0 9 7 12.32 7 5 0 N 15 6 5 0 B 15 5

H P 2 1 0 9 12.30 750 N 1 7 50 A 1 5

275

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HP211 9 12.38 750 N 1 750 E 1 5

HP212 9 12.60 750 N 1 750 A 1 2

HP218 9 12.08 750 N 15 750 C 15 5

HP219 9 12.65 750 N 15 650 C 15 5

HP220 7 12.26 750 N 15 650 C 15 5

HP221 7 12.70 750 N 15 750 C 15 5

HP222 9 12.50 750 N 15 750 A 15 5

HP224 9 12.67 750 N 15 750 B 15 5

HP225 9 12.44 750 N 15 750 C 15 5

HP226 9 12.65 750 N 15 750 D 15 5

HP227 9 12.60 750 N 15 750 B 15 10

HP228 7 12.55 750 N 15 750 B 15 10

HP229 9 12.66 750 N 15 750 D 15 5

HP230 7 12.50 750 N 15 750 D 15 5

HP231 9 12.60 750 N 15 750 C 15 10

HP232 7 12.45 750 N 15 750 C 15 10

HP233 7 12.42 750 N 1 750 A 1 2

HP235 7 12.42 750 N 1 450 A 1 2

HP236 7 12.75 750 N 1 650 A 1 2

HP237 7 12.68 750 N 1 550 A 1 2

HP238 7 12.73 750 N 1 750 F 1 2

HP240 7 12.47 750 N 15 750 A 15 2

Note:

Calcination : N - 100% Nj

Carbonation: A - 15% C02 / N2 B - 15% C02 / 10%H2O /N 2 C - 15% C02 / 10% HjO / 5% CO / 2.5% H2 / N2 D - 15% C02 / 10% H20 / 5% CO / 2.5% H2 / 0.22% H2S E - 15% C02 / 10% H20 / 20% CO / 10% H2 / N2

F - 25 % C 02 / N2

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Computer Program of Distributed Pore Size Model

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nnnnnonnonn ooooooooooo o oooo RMPG CRSMN (1981) CHRISTMAN P.G. FROM 0.461,0.525,0.581,0.672,0.684,0.692,0.693,0.694,0.694,0.702/ 0.7,0.9,1.1,1.7,2.2,2.7,3.2,4.7/ & & .651,.682,.686,.69,.696,.698,.7/ $ ,15.,18.,20./ $ 2.0,2.2,2.5,3.,4.,5.,6.,8.,10.,12.,15.,20./ $ .6, .77/ .764, $ .332,.377,.41,.444,.487,.530,.594,.694,.739,.747,.753,.76,.762, $ .713,.725,.731,.732,.733/ 8.6,10./ $ $ 4.8,6.8,9.8,11.8/ ,.652,.652,.654,.660,.662/ $ $ AA (YDATA(I),1=1,15)/0.,0.121,0.213,0.302,0.386, DATA MW/56./ DATA NPTR,NUM/50, 50/ DATA ,RPSQ(50),DELRP,DELRSQ COMMON/PELLET/RPEL(50) COMMON/PVAL/DPVAL(100),RPVAL(100),PPVAL(100) COMMON/PARAM/KRATE,ALPHA,DB,DK,DS,VR,CZERO,CBULK YDATA(600) XDATA(600), REAL LRATE(50) REAL RZSQ(50,2) REAL CONC(50),LRATE2(50)fLCONV(50),LPRSTY(50) REAL ,KG W KRATE,M REAL DIA(bO),CUMVOL(50),ETA(50),RZERO(50),R1(50) REAL AA (XDATA(I),I=l,15)/0.,1.,2.,3.,4.,5.,6.,7.,8.,9.,10.,12. DATA (XDATA(I),1=1,15)/0.,0.1,0.2,0.3,0.4,0.5,0.6, DATA (1)/0.0/ 1 R DATA NDIV COMMON/LENGTH/ COMMON/WORK/TAUFTR,CNVFTR,RTEFTR,RADFTR,EPSLN,FINFTR,FCORR COMMON/TIME/NTIME COMMON/FACTOR/TRTSTY COMMON/PROP/RZERO,RZSQ COMMON/VALUES/TVALUE(100),DVALUE(100),RVALUE(100),PVALUE(100) COMMON/COEFF/DEFF(50),RK(50) COMMON/TABLE/TTABLE(100,50),RTABLE(100,50),PTABLE(100,50) ,HEAD KEYS(20) CHARACTER*20 MPORE PROGRAM AA YAAI,=, )/0.,.5,.58,.62,.65,.68,.685,.7/ (YDATA(I),1=1,8 DATA )/0.,2.5,5.,7.5,10.,15.,20.,30./ (XDATA(I),1=1,8 DATA (YDATA(I),I=l,15)/0.,.1,.18,.254,.341,.446,.522,.584, DATA HTA 65 1AM 1%O/2 RN 10-12 RUN 10%CO2/N2, 1ATM, 655, BHATIA, (HP137) ATM 15 1%C02, 650C, (HP046) 1ATM 15%C02, 650C, NEE* NE, XAA IRE NXVCTR(20) IFREE, NXDATA, NSET, INTEGER*4 AA (XDATA(I),1=1,23)/0.,.1,.3,.5,.7,.9,1.,1.2,1.4,1.6,1.8, DATA 15 = IDATA AA XAAI),1=1,14)/0.,.1,.2,.3,.5,.8,1.3,1.8,2.8,3.8, (XDATA(I DATA (YDATA(I),I=l,13)/0.,.088,.147,.229,.361,.464,.551,.625, DATA (XDATA(I),I=l,13)/0.,.2,.3,.6,1.1,1.6,2.1,2.6,3.6,4.6,6.6, DATA (YDATA(I),I=l,23)/0.,.055,.088,.131,.180,.229,.248,.293, DATA (HP066) ATM 1 750C,15%C02, 15 IDATA= AA (YDATA(I),I=l,14)/0.,.3,.401,.484,.611,.628,.636,.638,.650 DATA 8 IDATA= 5C1%0, T (HP049) 1ATM 550C,15%C02, (HP043) 1ATM 5%C02, 650C, 23 IDATA= DT= 13 IDATA= "DISTRIBUTED PORE SIZE MODEL" SIZE PORE "DISTRIBUTED

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced $ .651,.682,.686,.69/ 12 IDATA= C $ C (XDATA(I),I=1,12)/0.,1.,2.,3.,4.,5.,6.,7.,8.,9.,10.,12./ DATA C 5 1 = IDATA C C ,.472,.526,.603,.645,.655,.655,.655/ .393,.43 $ C DT (YDATA(I),I=l,12)/0.,.1,.18,.254,.341,.446,.522,.584, DATA 0.461,0.525,0.581,0.672,0.684,0.692,0.693,0.694,0.694,0.702/ C 0.7,0.9,1.1,1.7,2.2,2.7,3.2,4.7/ 0.386, & (YDATA(I),1=1,15)/0.,0.121,0.213,0.302, DATA C & (XDATA(I),1=1,15)/0.,0.1,0.2,0.3,0.4,0.5,0.6, DATA C 1.1,1.2,1.4,1.6,1.8,2.,3./ 17 IDATA= C , ,.34 C .169,.22,.256,.30 (YDATA(I),I=l,17)/0.,.093,.129, DATA C $ C (HP141) 15ATM 650C,15%C02, C C C DATA (XDATA(I),I=l,17)/0., (XDATA(I),I=l,17)/0., DATA 14 C IDATA= C C C non ooo o o o o o o ooo DK,VR,VG,DIA,CUMVOL,RXNHRS,NPTS,DELX) 1 DT= IDATA+1 NDATA= RADFTR=3./TEMP2 RXNSEC=RXNHRS *RXNSEC=RXNHRS 3 RHO=MW*TEMPl/VR 600. VG*MW/TEMPI RTEFTR= l.-EPSLN TEMP1= CUMVOL(NPTS) EPSLN= PARAMETERS SECONDARY CALCULATE CBULK=CZERO READIN(PELLET,ALPHA,CZERO,KRATE,DS,TRTSTY,DB,KG, CALL PARAMETERS MODEL THE IN READ 100 = NDIV 25 = NTIME TEMP2=PELLET*PELLET*PELLET CNVFTR=TEMP1*(ALPHA-1.) AREA= RK(1)/KRATE/RHO AREA= FINFTR=KG*DELRP DELRP=PELLET/FLOAT(NPTR-1) VR*(ALPHA-1.)*KRATE*CZERO TAUFTR= CALL DIST(DIA,CUMVOL,NPTS,ETA,NTOT,NUM) CALL 1 NITER= PDE FOR CONSTANT OF VALUES INITIAL CALCULATE 2.*DELRP/PELLET) -(1.- FCORR= CZERO = CONC(NPTR) = CZERO DIFFEQ(CONC,CBULK,NPTR) CALL PROFILES INITIAL CALCULATE CALL START(NTOT,NPTR,TPLUG,RTEMAX,PELLET,LCONV,LPRSTY) CALL REACT(NTOT,RXNSEC) CALL EVOLVE(RZERO,NTOT,RXNSEC) CALL 0.0 TIME= CALL REACT(NTOT,RXNSEC) CALL EVOLVE(RZERO,NTOT,RXNSEC) CALL

.2,

.3,.4,.5, .6, .7, .8, .9,1.,

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CALL START(NTOT,NPTR,TPLUG,RTEMAX,PELLET,LCONV,LPRSTY) C C CALCULATE INITIAL PROFILES C CALL DIFFEQ(CONC,CBULK,NPTR) C AREA= RK(1)/KRATE/RHO DO 16 1=1,NPTR LRATE(I) = CONC(I)*RK(I)*RTEFTR 16 CONTINUE CALL FINISH(CONV,LCONV,RATE,LRATE,PRSTY,LPRSTY,RTEMAX,EFF,NPTR) WRITE(6,500) TPLUG,RXNSEC,AREA IF (TPLUG.LT.RXNSEC) RXNSEC=TPLUG CALL SHOW(TIME,CONV,RATE,EFF,PRSTY,CONC,DEFF, 1 LCONV,LRATE,LPRSTY,NPTR,NITER) XDATA(NDATA ) = 0. YDATA(NDATA )= 0. C NITER= 0 18 DELTM= DELX/RATE NDATA= NDATA+1 TEMP= TIME+DELTM IF{TEMP.LT.RXNSEC) GOTO 19 TEMP=RXNSEC DELTM=TEMP-TIME 19 CONTINUE TIME=TEMP 20 CALL DIFFEQ(CONC,CBULK,NPTR) C CZERO = CONC(NPTR) C WRITE(6,*) 'CONC(50) = ', CONC(NPTR) C DO 30 J=1,NPTR LRATE2(J) = LRATE(J) 30 CONTINUE CALL RESET(CONC,TIME,NPTR,DELTM,LCONV,LPRSTY,LRATE) NITER=NITER + 1 IF(NITER.GE.50) GO TO 50 DO 40 1=1,NPTR J=NPTR+1-I IF(LRATE(J).LE.0.0) GOTO 50 DRATE= ABS(LRATE2(J)-LRATE(J)) DFRAC= DRATE/LRATE(J) IF(DFRAC.GE.0.01 ) GOTO 20 40 CONTINUE 50 CALL FINISH(CONV,LCONV,RATE,LRATE,PRSTY,LPRSTY, 1 RTEMAX,EFF,NPTR) CALL SHOW(TIME,CONV,RATE,EFF,PRSTY,CONC,DEFF, 1 LCONV,LRATE,LPRSTY,NPTR,NITER) XDATA(NDATA) = TIME/60. YDATA(NDATA) = CONV C ADATA(NDATA) = CONC(l) C BDATA(NDATA) = CONC(NPTR) IF(TIME.LT.RXNSEC) GOTO 18 DUMMY = NDATA-IDATA IF(DUMMY.GE.MAX) MAX= DUMMY NXDATA= MAX C XDATA(NDATA+DUMMY*1) =0. C YDATA(NDATA+1) = 0. NXVCTR(l) = IDATA NXVCTR(2) = DUMMY C NXVCTR(3) = 1

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NSET= 2 IFREE = 1 CALL GRAPHF( XDATA, YDATA, KEYS, HEAD, NSET, NXDATA, IFREE, & NXVCTR ) C 500 FORMAT(1H1,9X,'TPLUG=',E12.5,IX,'RXNSEC=',E12.5,2X, 1 'AREA(CM2/G)= ',E12.5) STOP END

SUBROUTINE READIN(PELLET,ALPHA,CZERO,KRATE,DS,TRTSTY,DB,KG, 1 DK,VR,VG,DIA,CUMVOL,RXNHRS,NPTS,DELX) C C THIS SUBROUTINE READS THE MODEL PARAMETERS INTO THE COMPUTER C AND GENERATES AN ECHO PRINT C REAL KRATE,KG,MWC02,MWN2,MWGAS,MWAIR,MW REAL DIA(50), CUMVOL(50), DATA(17) INTEGER GAS, AIR COMMON/PRINT/IPRINT DATA NUM/50/ C DATA PRESS/1./ DATA MWC02,TC02,MWN2,TN2,MWAIR,TAIR/44.,3.996,28.,3.681, 1 29.,3.617/ C DATA PRESS/1./ C DATA MWS02,TS02,MWN2,DVN2,MWAIR,DVAIR/64.,41.1,28.,17.9, C 1 29.,20./ DATA AIR/3 / DATA RG/82.057/ DATA MW/56.0/ C C PELLET= RADIUS OF PELLET (CM) C ALPHA= RATIO OF THE MOLAR VOLUMES OF THE PRODUCT C AND THE REACTANT C CZERO= CONC. OF GAS REACTANT (MOLES/CM3) C KRATE= SURFACE REACTION RATE CONSTANT (CM/SEC) C DS = DIFF. OF THE GAS REACTANT THROUGH THE PRODUCT C LAYER (CM2/SEC) C TRTSTY = TORTUOSITY THROUGH THE POROUS MEDIUM C DB = BULK DIFF. OF THE GAS REACTANT (CM2/SEC) C DK = KNUDSEN DIFFUSIVITY/PORE RADIUS (CM/SEC) C VR= MOLAR VOLUME OF THE REACTANT(CM3/MOLE) C DIA = VECTOR CONTAINING THE DIAMETER OF THE PORES FROM THE C MEASURED PORE SIZE DISTRIBUTION (MICRONS), (CM) C CUMVOL = VECTOR CONTAINING THE CUMULATIVE VOLUME OF ALL C PORES LARGER THAN THE CORRESPONDING VALUE OF DIA C (CM3/GM), (CM3/CM3) C RXNHRS= REACTION TIME OF INTEREST (HRS) C NPTS= NUMBER OF VALUES IN THE VECTORS DIA, AND CUMVOL C DELX = THE DESIRED INCREMENT IN CONVERSION FOR EACH TIME C STEP, IN GENERAL THE ACTUAL CHANGE IN CONVERSION C WILL BE LESS THAN THIS VALUE C VG= VOLUME OF PURE REACTANT PER GRAM C KG= MASS TRANSFER COEFF. OUTSIDE THE PELLET (MOLES/CM2/SEC) C C IPRINT DETERMINES THE LEVEL OF OUTPUT ON FILE OUTPUT C IF(IPRINT.EQ.0) OUTPUT CONTAINS THE MACROSCOPIC PROPERTIES C OF THE PELLET AS A FUNTION OF TIME C IF(IPRINT.EQ.l) OUTPUT CONTAINS THE NORMAL OUTPUT C IF(IPRINT.EQ.2) OUTPUT CONTAINS THE MACROSCOPIC PROPERTIES

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced ILG 1 IFLAG= 4 RA(,) DIA(I),CUMVOL(I) READ(5,*) 3 onnnooonnoo oo to m oooo VG=1./DATA(11) DATA(2) ALPHA= *DATA(3) DATA(12) = KG KG=DATA(12)*DATA(7)*DATA(3)/DATA(1)/2. TAUAB*TAUAB TAUSQR= VR=DATA(9) DATA(8) DK= DATA(6) TRTSTY= DATA(5) DS= DATA(4) KRATE= 1.08/15. DATA(7)= (TC02+TGAS)/2. TAUAB= (MWC02*MWGAS)) DTEMP1=SQRT((MWC02+MWGAS)/ ED5* LNPTS READ(5,*) ED5* GAS READ(5,*) MWGAS=MWN 2 DATA(7)= 0.00158583*DTEMP1/DTEMP2 DATA(7)= PRESS*TAUSQR*XOMEGA DTEMP2= XOMEGA=0.7896 DMAX=DATA(14) VG DATA(11)= RXNHRS=DATA(10) DB=DATA(7) CZERO=DATA(3) 0.00002 DATA(7)= 1.08 DATA(7)= DTEMP1* DTEMP1= SQRT(TEMP * * 3) 9700.*SQRT(TEMP/MWC02) DATA(8)= DATA(17))/TEMP/RG - (DATA(3)*PRESS = DATA(3) PELLET=DATA(1) DELX=DATA(15) +273.16 TEMP=DATA(13) CUMVOL(1)=SLOPE*ALOG(DMAX/DIA(1))+CUMVOL(1) 3 GOTO DIA(2) DIA(1)= 1=2,ISTOP 7 DO DIA(1),CUMVOL(1) READ(5,*) NSAVE=LNPTS-1 TGAS=TN2 IPRINT READ(5,*) 1=9,17 2 DO CONTINUE 1=1,7 1 DO PRESS= DATA(16) PRESS= SLOPE=(CUMVOL(2)-CUMVOL(1))/ALOG(DIA(2)/DIA(1)) CUMVOL(2) = CUMVOL(1) LNPTS=LNPTS-1 CONTINUE FGSE.I) TGAS=TAIR IF(GAS.EQ.AIR) FGSE.I) MWGAS=MWAIR IF(GAS.EQ.AIR) IF(DIA(I).LE.DMAX) GOTO 4 GOTO IF(DIA(I).LE.DMAX) IF(IFLAG.GT.O) GOTO 5 GOTO IF(IFLAG.GT.O) ISTOP=LNPTS IFLAG=0 PRINT ECHO NO IS THERE IF(IPRINT.NE.l) ED5* DATA(I) READ(5,*) ED5* DATA(I) READ(5,*)

PRXMTO FTE PELLET THE OF APPROXIMATION AT EVERY GRID POINT IN THE FINITE DIFFERENCE FINITE THE IN POINT GRID EVERY AT

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CSAVE= CUMVOL(1) CUMVOL(1) = 0.0 DIA( 1)= DMAX 5 CUMVOL(I)=CUMVOL(I)- CSAVE 7 CONTINUE NPTS= LNPTS C C ECHO PRINT C IF(IPRINT.NE.l) GOTO 9 WRITE(6,200) DATA(13) WRITE(6,205) (DATA(I) , 1=1,12) WRITE(6,210) LNPTS,NUM,DELX WRITE(6,215) 9 CONTINUE C C CONVERT FROM MICRONS TO CM C XSOLV= CUMVOL(1) FTR= VG+ (CUMVOL(LNPTS) -XSOLV) DO 10 1=1,LNPTS DIA(I)= DIA(I)*0.0001 CUMVOL(I) =(CUMVOL(I)-XSOLV)/FTR 10 CONTINUE IF(IPRINT.EQ.1) WRITE(6,230) IF(IPRINT.EQ.1) WRITE(6,240) (DIA(I),CUMVOL(I),1=1,LNPTS) 200 FORMAT(30X,'MULTIPLE PORE MODEL'//,30X, 1 'TEMPERATURE(DEG C)=',F8.1,18X,//18X,'INPUT DATA') 205 FORMAT(/10X,'PELLET RADIUS(CM)= ',E12.5/10X, A 'RATIO OF MOLAR VOLUMES= ',F12.4/10X, 1 'BULK C02 CONCENTRATION(MOLES/CC)= ',E12.5/ B 10X,'REACTION RATE CONCTANT(CM/SEC)= ',E12.5/ C 10X,'PRODUCT LAYER DIFFUSIVITY(CM2/SEC)= ',E12.5/ D 10X,'PELLET TURTUOSITY FACTOR= ',F12.2/ E 10X,'BULK DIFFUSIVITY (CM2/SEC)= ',E12.5/ F 10X,'KNUDSEN DIFFUSION COEFF. (CM/SEC)= ',E12.5/ G 10X,'REACTANT MOLAR VOLUME= ',F12.4/ H 10X,'REACTION TIME(HRS)= ',F12.4/ I 10X,'VOLUME PER GRAM OF SOLID(CM3/GM)= ',F12.4/ J 10X,'MASS TRANSFER COEFF.= ',F10.5) 210 FORMAT(/10X,'TOTAL NUMBER OF DATA POINTS= ',15/ A 10X,'MAXIMUM NUMBER OF DIVISION= ',15/ B 10X,'CONVERSION INCREMENT= ',F5.3) 215 FORMAT(//10X,5(A6)//10X,'DIAMETER(MICRON)= ',3X, 1 'CUMULATIVE VOLUME(CM3/GM)= '/) 230 FORMAT(//10X,'DIAMETER(CM)=',7X,'CUMVOLUME(CM3/CM3)'/) 240 FORMAT(10X,E12.5,10X,F10.4) RETURN END C C SUBROUTINE DIST(DIA,CUMVOL,NPTS,ETA,NTOT,NUM) C C THIS SUBROUTINE GENERATES RZERO AND ETA FROM THE MEASURED PORE C SIZE DISTRIBUTION. IT INTERPOLATE BETWEEN DATA POINTS C REPRESENTED BY DIA AND CUMVOL BY ASSUMING THAT CUMVOL IS C A LINEAR FUNCTION OF LOG(DIA). C NTOT IS DETERMINED BY DIVIDING EACH SECTION INTO AN EQUAL CC NUMBER OF SMALLER INTERVALS DETERMINED SUCH THAT C (NTOT.LE.NUM). C ETA IS ASSUMED TO BE A CONSTANT OVER EACH INTERVAL (R-DELTA R) C TO R.

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REAL DIA(50),CUMVOL(50), ETA(50) REAL RTEMP(50), VTEMP(50) REAL FRACV(50), LOGRT(50),LSLOPE(50) COMMON/FACTOR/TRTSTY COMMON/TOTAL/ETASUM(50),EZERO(50),ETATOT COMMON/PROP/RZERO(50),RZSQ(50,2) COMMON/PRINT/IPRINT DATA Z/0.5773503/

C DIA = VECTOR CONTAINING THE DIAMETER OF THE PORES FROM THE C MEASURED PORE SIZE DISTRIBUTION (MICRONS), (CM) C CUMVOL = VECTOR CONTAINING THE CUMULATIVE VOLUME OF ALL C PORES LARGER THAN THE CORRESPONDING VALUE OF DIA C (CM3/GM), (CM3/CM3) C ETA = VECTOR CONTAINING NUMBER OF PORES WITH RADIUS BEWEEN C (R-DELTA R) AND R PER UNIT RADIUS, PER UNIT AREA C NTOT = DIMENSION OF ETA C NUM = MAXIMUM VALUE OF NTOT C LOCNPT= NPTS NACT=(NUM-1)/(LOCNPT-1) FACT=FLOAT(NACT) NTOT=NACT*(LOCNPT-1) +1 LCNTOT=NTOT DO 5 1=1,LOCNPT INV=LOCNPT+1 - I RTEMP(I)= DIA(INV)/2. LOGRT(I)= ALOG(RTEMP(I)) VTEMP(I) = CUMVOL(LOCNPT)-CUMVOL(INV) 5 CONTINUE FRACV(1)= 0. DO 7 I=2,LOCNPT LSLOPE(I)= (VTEMP(I)-VTEMP(1-1))/(LOGRT(I)-LOGRT(1-1)) 7 CONTINUE RZERO(1)=RTEMP(1) ETA(1)=0. DO 20 I=2,LOCNPT IKOUNT=l+(1-1)*NACT RZERO(IKOUNT)=RTEMP(I) JSTART=(IKOUNT-NACT)+1 JSTOP=IKOUNT JKOUNT=NACT-1 STEP=(RTEMP(I)-RTEMP(1-1))/FACT DO 10 J=J START,JSTOP RZERO(J)=RTEMP(I)-(FLOAT(JKOUNT)*STEP) CALL EFUN(RZERO(J-l),RZERO(J),FRACV(J),LSLOPE(I),ETA(J)) JKOUNT=JKOUNT-1 10 CONTINUE 20 CONTINUE ETASUM(1)=0. ETATOT = 0. EZERO(l)=ETA(l) C C ETA(I)*DEL(RZERO) = # OF PORES WITH SIZES BETWEEN C RZERO AND (RZERO+DRZERO) DO 30 1=2,LCNTOT DELRZ=RZERO(I)-RZERO(1-1) ETASUM(I)=ETA(I)*DELRZ EZERO(I)=ETA(I) ETATOT=ETATOT+ETASUM(I) 30 CONTINUE

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DO 40 I=2,LCNTOT ZTEMP1=Z*(RZERO(I)-RZERO(I—1)) ZTEMP2=RZERO(1-1)+RZERO(I) RZT1={ZTEMP2-ZTEMP1)/2. RZT2=(ZTEMP2+ZTEMP1)/2. RZSQ(I,1)=RZT1*RZT1 RZSQ(I,2)=RZT2*RZT2 40 CONTINUE IF(IPRINT.EQ.l) WRITE(6,499) IF(IPRINT.EQ.l) WRITE(6,500) (RZERO(I) ,ETASUM(I) ,ETA(I) , 1 I=l,LCNTOT) 499 FORMAT(lHl,13X,'RZERO',12X,'ETASUM',14X,'EZERO'/) 500 FORMAT(3(8X,E12.5)) RETURN END Q ********************************************* SUBROUTINE EVOLVE(RZERO,NTOT,TAUMAX) C ********************************************* c C THIS SUBROUTINE GENERATES THE VALUES STORED IN COMMON BLOCK C /TABLE/. FROM THE VALUES STORED IN RTABLE A CUBIC SPLINE IS C FIT TO INTERPOLATE R1 AS A FUNCTION OF TAU C REAL RZERO(50) COMMON/TABLE/TTABLE(100,50),RTABLE(100,50),PTABLE(100,50) COMMON/TIME/NTIME COMMON/LENGTH/NDIV DATA EXPNT/3./ DATA IOPT/0/ C C RZERO= VECTOR CONTAINING THE INITIAL VALUES OF THE PORE RADII C NTOT= DIMENSION OF VECTOR RZERO C TAUMAX=MAXIMUM VALUE OF TAU THAT IS OF INTEREST IN THIS C SIMULATION C TAULO=TAUMAX*1.05 TAUHI=TAULO*l.01 TAUMED=TAULO*1.005 LNTOT=NTOT NDIVL1=NDIV-1 DO 20 1=1,LNTOT RTABLE(1,1)=RZERO(I) TTABLE(1,1)=0. DO 10 J=2,NDIV FACTOR=FLOAT(NDIV-J)/FLOAT(NDIVL1) RTABLE(J,I)=RZERO(I)*(FACTOR* *(1./EXPNT)) TTABLE(J,I)=FTAU(RTABLE(J,I),RZERO(I)) 10 CONTINUE CALL SPLINE(TTABLE(1,1),RTABLE(1,1),PTABLE(1,1),NDIV,IOPT) IF(TTABLE(NDIV,I).GT.TAULO) GO TO 30 20 CONTINUE RETURN 30 CONTINUE ISTART=I+1 IF(ISTART.GT.LNTOT) RETURN DO 50 I1=1START,LNTOT RGUES1 =0. TGUES1=FTAU(0.0,RZERO(II)) RGUES2=RZERO(II) TGUES2=0. 35 CONTINUE SLOPE=(RGUES1-RGUES2)/(TGUES1-TGUES2)

nano on CONTINUE 50 CONTINUE 40 7 CONTINUE 37 noonnonnnnnnn CONTINUE 36 O AASOE I H ETR V YV XV, VECTORS THE SPLINE IN CUBIC STORED DATA INTERPOLATING FOR AN CALCULATES SUBROUTINE THIS NDIV= DIMENSION OF THE VECTORS THE OF DIMENSION NDIV= VALUES X THE CONTAINING XV=VECTOR PV=VECTOR CONTAINING THE VALUES OF THE 2ND DERIVATIVE OF THE OF DERIVATIVE 2ND THE OF VALUES THE CONTAINING PV=VECTOR VALUES Y THE CONTAINING YV=VECTOR IF(IOPT.EQ.l) THE 2ND DERIVATIVES AT THE END POINTS ARE SET ARE POINTS END THE AT DERIVATIVES 2ND THE IF(IOPT.EQ.l) F IP.QO TE N EIAIE TTEEDPIT R SET ARE POINTS END THE AT DERIVATIVES 2ND THE (IOPT.EQ.O) IF O1 1=1,LIM 10 DO LIM=NDIV-1 IFIRST/2/ DATA C/100*1.0/ DATA XV(100),YV(100),PV(100) REAL O2 1=2,LIM 20 DO A(100),B(100),C(100),D(100),H(100) REAL RETURN END SPLINE(TTABLE(1,11),RTABLE(1,11),PTABLE(1,11),NDIV,IOPT) CALL URUIE SPLINE(XV,YV,PV,NDIV,IOPT) SUBROUTINE TTABLE(J,II)=FTAU(RTABLE(J,II),RZERO(II)) RTABLE(J,II)=((DIFFSQ*FACTOR)+RMINSQ)**(1./EXPNT) J=2,NDIV 40 DO FACTOR=FLOAT(NDIV-J)/FLOAT(NDIVL1) TTABLE(1,II)=0.0 RTABLE(1,11)=RZERO(II) DIFFSQ=RZSQ-RMINSQ RZSQ=RZERO(II)**EXPNT 35 TO GO RMINSQ=RGUES3 RMINSQ=RGUES3 * *EXPNT TGUES1=TGUES3 RGUES1=RGUES3 GOTO 35 GOTO TGUES2=TGUES3 RGUES2=RGUES3 RGUES3=SL0PE*(TAUMED-TGUES2)+RGUES2 TGUES3=FTAU(RGUES3,RZERO(II)) IF(TGUES3.LE.TAUHI) GO TO 37 TO GO IF(TGUES3.LE.TAUHI) IF(TGUES3.GT.TAULO) GOTO 36 GOTO IF(TGUES3.GT.TAULO) A(I)=H(I-1)/H(I) TM1( (1+1)-YV(I))/H(I) V DTEMP1=(Y I = 6.*(DTEMP1-DTEMP2)/H(I) (I) = D (I)-YV(1-1))/H(1-1) V DTEMP2=(Y B(I)=2.*(H(I)+H(I-1))/H(I) IF(IOPT.EQ.0) GO TO 30 TO GO IF(IOPT.EQ.0) INTERPOLATING CUBIC SPLINE CUBIC INTERPOLATING H(I)=XV(1+1) - XV(I) - H(I)=XV(1+1) EQUAL TO THE VALUE AT THEIR NEAREST NEIGHBOR NEAREST THEIR AT VALUE THE TO EQUAL ZERO TO EQUAL

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C 0 CONTINUE 30 WIE6* , TVALUE(I) I, WRITE(6,*) C CONTINUE 5 0 CONTINUE 20

5 CONTINUE 25 CONTINUE 10 ooo oooooooo 0 CONTINUE 30 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ★ I THIS SUBROUTINE CALCULATES THE VALUES OF THE DIFFUSIVITY, THE OF VALUES THE CALCULATES SUBROUTINE THIS NITROAIGCBCSLN O AHPOET N STORES AND PROPERTY EACH FOR SPLINE CUBIC INTERPOLATING AN THE 2ND DERIVATIVERS IN /PVAL/. IN DERIVATIVERS 2ND THE CALCULATES IT BLOCK/VALUES/. STORES COMMON AND THE IN TAU OF RESULTS FUNCTION THE A AS POROSITY AND REACTIVITY, RT(,0) DV LNTOT NDIV, WRITE(6,200) O3 1=1,NDIV 30 DO COMMON/PRINT/IPRINT COMMON/PARAM/KRATE,ALPHA,DB,DK,DS,VR,CZERO,CBULK COMMON/PVAL/DPVAL(100),RPVAL(100),PPVAL(100) COMMON/TABLE/TTABLE(100,50),RTABLE(100,50),PTABLE(100,50) ETA(50) (50), R1 REAL NCHECK=NDIV/LNTOT - A H P EFTR=1.-EPSLN L A = R T F A T O T N = T O T N L IOPTl/O/ DATA COMMON/LENGTH/NDIV COMMON/WORK/TAUFTR,CNVFTR,RTEFTR,RADFTR,EPSLN,FINFTR,FCORR COMMON/VALUES/TVALUE(100),DVALUE(100),RVALUE(100),PVALUE(100) O1 1=1,LNTOT 10 DO STOP 5 GOTO IF(NCHECK.EQ.2) RETURN PV(NDIV)=PV(LIM) PV(1)=PV(2) (2•*H(LIM-1)*3.*H(LIM))/H(LIM) B(LIM)= (2)=(3.*H(1)+2.*H(2))/H(2) B SUBROUTINE REACT(NTOT,RXNSEC) SUBROUTINE O2 11TR, NDIV 1=1START, 20 DO ) I , C N I ( E L B A T T = ) C N I ( E U L A V T TVALUE(INCL1)=TTABLE(INCL1,I) INC=I*2 FTAU(NO)G.XSC TVALUE(LNTOT)=RXNSEC*1.02 IF(TVALUE(LNTOT).GT.RXNSEC) TVALUE(LNTOT-1)=RXNSEC*1.01 .RXNSEC) T IF(TVALUE(LNTOT-1).G INCL1=INC-1 ISTART=(2 ISTART=(2 * LNTOT)+1 IF(ISTART.GT.NDIV) GO TO 25 TO GO IF(ISTART.GT.NDIV) END RETURN PV(NDIV)=0. PV(1)=0. TRIDAG(IFIRST,LIM,A,B,C,D,PV) CALL CALL TRIDAG(IFIRST,LIM,A,BfC,D,PV) CALL

TVALUE(I)= TTABLE(I,LNTOT) TVALUE(I)= CALL SPLINE(TVALUE,DVALUE,DPVAL,NDIV,IOPT1) CALL AL NER,T,VLEI,VLEI,VLEI),LNTOT) INTE(R1,ETA,DVALUE(I),RVALUE(I),PVALUE(I CALL LOOK(TVALUE(I),R1,ETA,LNTOT) CALL

1 .

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced POETE FTE OOSMDU SUIGTA H ELT IS PELLET ISOTROPIC. THE THAT INITIALLY ASSUMING C MEDIUM MACROSCOPIC POROUS THE OF THE OF VALUES THE C PROPERTIES ALL INITIALIZE SUBROUTINE C THIS C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c * C ***************************************************************** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Q 200 FORMAT(///15X,'THE TOTAL NUMBER OF PORE RADII CAN BE DIVIDED'/ BE CAN RADII PORE OF NUMBER TOTAL FORMAT(///15X,'THE 200 100 FORMAT(10X,'TAU',10X,'DIFFUSIVITY',10X,'RATE CONST.', FORMAT(10X,'TAU',10X,'DIFFUSIVITY',10X,'RATE CONTINUE 100 40

noooononooonon FORMAT(4(5X,E12.5)) 105 LPRSTY= VECTOR CONTAINING THE VALUE OF THE LOCAL POROSITY LOCAL THE OF VALUE THE CONVERSION CONTAINING LOCAL THE VECTOR OF VALUE LPRSTY= THE CONTAINING VECTOR LCONV= PELLET THE OF RADIUS = PELLET THE IN CONVERSION, ZERO AT RATE, REACTION MAXIMUM THE RMAX= TPLUG= THE TIME IT TAKES FOR ALL THE PORES AT THE OUTSIDE THE AT PORES THE ALL FOR TAKES IT TIME THE TPLUG= DIFFERENCE FINITE IN POINTS GRID OF NUMBER THE NPTR= ETA VECTOR THE OF SIZE NTOT= BETWEEN RADII WITH PORES OF NUMBER THE CONTAINING VECTOR = ETA 2 15X,'THAN TWO.'/15X,'NTOT',14/) 15X,'THAN 2 1 15X,'INTO THE NUMBER OF TAU VALUES BY A VALUE OTHER', VALUE A BY VALUES TAU OF NUMBER THE 15X,'INTO 1 10X,'POROSITY'/) 1 RT(,) REA= ',RMAX 'RTEMAX= WRITE(6,*) K1 =A3 RK(1) A1 DEFF(1)= RT(,0) TAU()DAU()RAU( ),PVALUE(I),1=1,NDIV) (TVALUE(I),DVALUE(I),RVALUE(I WRITE(6,105) SUBROUTINE START(NTOT,NPTR,TPLUG,RMAX,PELLET,LCONV, LPRSTY) START(NTOT,NPTR,TPLUG,RMAX,PELLET,LCONV, SUBROUTINE O2 1=2,NPTR 20 DO RMAX=A3*CZERO*RTEFTR DELRSQ=DELRP*DELRP 0. RPSQ(1)= 0. RPEL(1)= LCONV{1)=(EPSLN-LPRSTY(1))/CNVFTR LPRSTY(1)=PVALUE(1) A3=RVALUE(1) A1=DVALUE{1) DATA RANGE/.999/ DATA COMMON/COEFF/DEFF(50),RK(50) COMMON/VALUES/TVALUE(100),DVALUE(100),RVALUE(100),PVALUE(100) COMMON/WORK/TAUFTR,CNVFTR,RTEFTR,RADFTR,EPSLN,FINFTR,FCORR COMMON/PROP/RZERO(50),RZSQ(50,2) COMMON/PARAM/KRATE,ALPHA,DB,DK,DS,VR,CZERO,CBULK COMMON/PELLET/RPEL(50),RPSQ(50),DELRP,DELRSQ KRATE REAL LCONV(50),ETA(50),LPRSTY(50) REAL FLOV1.E1E1) CN() 0. LCONV(l)= IF(LCONV(1).LE.1.E-12) CN( )=LCONV(1) LCONV(I RESISTANCE DIFFUSIONAL OF ABSENCE RK(I) = A3 = RK(I) )=A1 DEFF(I RPEL(I)=PELLET*FLOAT(I—1)/FLOAT(NPTR-1) REPRESENTATION OF P\THE PELLET P\THE OF REPRESENTATION END RETURN WRITE(6,100) (Rl-DELTA Rl) AND R1 PER UNIT RADIUS PER UNTI AREA UNTI PER RADIUS UNIT PER R1 AND Rl) (Rl-DELTA OF THE PELLET TO PLUG TO PELLET THE OF CALL SPLINE(TVALUE,PVALUE,PPVAL,NDIV,IOPT1) CALL SPLINE(TVALUE,RVALUE,RPVAL,NDIV,IOPT1) CALL IF(IPRINT.NE.l) GO TO 40 TO GO IF(IPRINT.NE.l)

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced

nnnnonn oooooo m oooo o o o o o o o o 0 CONTINUE 20 NDIM = SIZE OF VECTORS Rl AND ETA AND Rl VECTORS OF SIZE = NDIM A FUNCTION OF TAU. GIVEN A VALUE OF Rl, ETA IS CALCULATED IS ETA Rl, OF VALUE A GIVEN TAU. OF FUNCTION A ETA = VECTOR WHICH CONTAINS THE NUMBER OF PORES WITH RADII WITH PORES OF NUMBER THE CONTAINS RADII INNER WHICH THE OF VECTOR = VALUES ETA THE CONTAINS WHICH TIME TO VECTOR = RESPECT Rl WITH (C/CZERO) OF INTEGRAL = TAU THIS SUBROUTINE USES SPLFUN TO INTERPOLATE VALUES OF Rl AS Rl OF VALUES INTERPOLATE TO SPLFUN USES SUBROUTINE THIS UHTA H OUAINBLNE ISOBEYED BALANCE POPULATION THE THAT SUCH RZERO= VALUE OF THE INITIAL PORE RADIUS PORE INITIAL THE OF PORE VALUE THE OF RZERO= RADIUS INNER THE OF VALUE = Rl HSFNTO ACLTS H AU FTUFO H INITIAL THE FROM TAU OF VALUE THE CALCULATES FUNCTION THIS (RZERO) AND INNER (Rl) RADII OF A PORE. A OF (Rl) RADII INNER AND (RZERO) /XLAMBDA/KRATE 1 RETURN DUM*ALOG(ALPHA/(ALPHA-1.)) + FTAU=FTAU RZERO*RZERO*ALPHA/4./XLAMBDA/DS DUM= RETURN SUBROUTINE LOOK(TAU,Rl,ETA,NDIM) SUBROUTINE FTAU=RZERO/XLAMBDA/KRATE FTAU=DUM3+DUM4*(DUM5-DUM6) DUM6=(DUM2-ALPHA)*ALOG((DUM2-ALPHA)/(1.-ALPHA)) DUM5=DUM2*ALOG(DUM2) DUM4=RZERO*RZERO/4./XLAMBDA/DS U3(.APA*ZR*1- (ALPHA-DUM2)/(ALPHA-1.)) DUM3=(1.-ALPHA)*RZERO*(1.- DUM2=DUM1*DUM1 DUM1=(Rl/RZERO) (BETA1/BETA2)*VR*CZERO*(ALPHA-1.) XLAMBDA= BETA2=1. BETA1=1. IF(DUM1.LE.0.0) GO TO 10 TO GO IF(DUM1.LE.0.0) END RETURN TPLUG=FTAU(0.0,RZERO(NTOT))*RANGE ELEA5)Rl(50) l ETA(50),R REAL COMMON/LENGTH/NDIV COMMON/TOTAL/ETASUM(50),EZERO(50),ETATOT COMMON/TABLE/TTABLE(100,50),RTABLE(100,50),PTABLE(100,50) END REAL KRATE REAL COMMON/WORK/TAUFTR,CMVFTR,RTEFTR,RADFTR,EPSLN,FINFTR,FCORR COMMON/PARAM/KRATE,ALPHA,DB,DK,DS,VR,CZERO,CBULK FUNCTION FTAU(R1,RZERO) FUNCTION CALCULATE THE PORE PLUGGING TIME FOR THE LARGEST PORES LARGEST THE FOR TIME PLUGGING PORE THE CALCULATE O1 1=1,LCNDIM 10 DO NDIVL1=NDIV-1 LCNDIM=NDIM TLOC=TAU PQI=PLI*PLI) RPSQ(I)=RPEL(I)*RPEL(I )=LPRSTY(1) LPRSTY(I BETWEEN (Rl-DELTA Rl) AND Rl, PER UNIT RADIUS,PER UNIT AREA UNIT RADIUS,PER UNIT PER Rl, AND Rl) (Rl-DELTA BETWEEN

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IF(TLOC.LT.TTABLE(NDIV,I)) GO TO 20 Rl (I) = 0. ETA(I) = 0. 10 CONTINUE RETURN 20 CONTINUE DO 50 J=I,LCNDIM DO 30 K=2,NDIV IF(TLOC.LE.TTABLE(K,J)) GO TO 40 30 CONTINUE WRITE(6,910) TLOC,NDIV,J,TTABLE(NDIV,J) Rl (J) = RTABLE(NDIV,J) GO TO 50 40 CONTINUE KK=K-1 Rl(J) =SPLFUN(TLOC,TTABLE(KK, J),TTABLE(KK+1,J ), 1 RTABLE(KK,J),RTABLE(KK+1,J),PTABLE(KK,J),PTABLE(KK+1,J)) 50 CONTINUE IF(TLOC.GE.TTABLE(NDIV,1)) GO TO 51 ETA(I) = 0. GO TO 59 51 EPSLN= TTABLE(NDIV,I)*0.001 TAU1=TTABLE(NDIV,I) TAU2= TTABLE(NDIV,1-1) RZER01=RTABLE(1,1) RZER02=RTABLE(1,1-1) 52 TEMP1=TAU1-TAU2 TEMP2= TAU1-TLOC TEMP3=RZER01-RZER02 RPLUG=RZER01-(TEMP3*TEMP2/TEMPI) TGUESS=FTAU(0.0,RPLUG) ERROR= TGUESS-TLOC AERROR=ABS(ERROR) IF(AERROR.LE.EPSLN) GO TO 58 IF(ERROR.LT.0.0) GO TO 56 RZER01=RPLUG TAU1=TGUESS GO TO 52 56 RZER02=RPLUG TAU2=TGUESS GO TO 52 58 WT=(RTABLE(1,1)-RPLUG)/(RTABLE(1,1)-RTABLE(1,1-1)) ETSMTP=ETASUM(I)*WT ETA(I)= ETSMTP/R1(I) IF(I.EQ.LCNDIM) GO TO 70 59 IPLUS=I + 1 DO 60 L=IPLUS,LCNDIM DELR=R1(L) -Rl(L-l) ETA(L)=ETASUM(L)/DELR 60 CONTINUE 70 CONTINUE 910 FORMAT(///20X,'TAU IS TOO LARGE'/20X,'TAU= ',E12.5/ 1 20X,'TABLE(',13,',',13,')= *,E12.5) RETURN END C FUNCTION SPLFUN(XVAL,XI,XIP1,YI,YIP1,PI,PIP1) C C THIS FUNCTION INTERPOLATES A VALUE GIVEN AN X VALUE AND THE C APPROXIMATE CONSTANTS NECESSARY TO EVALUATE A CUBIC SPLINE. C C XVAL= ARGUMENT OF THE SPLINE FUNCTION

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced C XIPl AT EVALUATED FUNCTION THE XI OF AT DERIVATIVE EVALUATED 2ND PIP1= FUNCTION THE OF XIP1 AT DERIVATIVE 2ND = PIEVALUATED FUNCTION THE C OF VALUE XI YIP1= AT C EVALUATED FUNCTION YI THE OF VALUE = C X OF C VALUE LOWER XI= C C X OF VALUE UPPER XIP1= C NEWVAL C CONCENTRATION THE ON AT BASED TAU OF PELLET THE INVALUE THE POINT CALCULATES EACH SUBROUTINE THIS C C C C C OF CONVERSION, DIFFUSIVITY, POROSITY AND REACTIVITY USING REACTIVITY AND POROSITY DIFFUSIVITY, VALUES CONVERSION, THE OF OBTAINS THEN REACTANT. GAS THE OF C HISTORY C oonnoonono oooo THIS SUBROUTINE CALCULATES ETA GIVEN THE VOID VOLUME OF ALL OF VOLUME VOID THE GIVEN ETA CALCULATES SUBROUTINE THIS PORES WITH RADII BETWEEN XLO AND XHI AND XLO BETWEEN RADII WITH PORES ETA= NUMBER OF PORES WITH RADII BETWEEN XLO AND XHI PER UNIT PER XHI AND XLO BETWEEN RADII WITH PORES OF NUMBER ETA= RADIUS PORE THE OF VALUE LOWER XLO= FRAVOL= FRACTION OF THE VOID VOLUME CONTAINED IN CONTAINED WITH PORES VOLUME VOID THE OF FRACTION FRAVOL= RADIUS PORE THE OF VALUE UPPER XHI= Bl= SLOPE OF THE LINE ON A PLOT OF CUMULATIVE VOLUME VOLUME VS. CUMULATIVE OF PLOT A ON LINE THE OF SLOPE Bl= FDL1L..-2 DELX1=0. IF(DELX1.LE.1.E-12) FDL2L..-2 DELX2=0. IF(DELX2.LE.1.E-12) XL02=XL0*XL0 FRAVOL=Bl*ALOG(XHI/XLO) DELX=XHI-XLO XL03=XL02*XL0 XHI3=XHI2*XHI XHI2=XHI*XHI END RETURN ETA=ETA2 ETA2=3.*FRAVOL/PI/ETEMP ETEMP=XHI3-XL03 SUBROUTINE RESET(CONC,TIME,NPT,DELTM,LCONV,LPRSTY,LRATE) SUBROUTINE SUBROUTINE EFUN(XLO,XHI,FRAVOL,B1,ETA) SUBROUTINE DATA PI/3.14159/ DATA END TEMP5=TEMP1+TEMP2+TEMP3+TEMP4 TEMP4=(Yl-(P1*HI))*DELX2 TEMP3=(Y2-(P2*HI))*DELX1 TEMP1=P1*DELX23/HI Y1=YI/HI HI=XIPl-XI DELX23=DELX2*DELX2*DELX2 DELX2=XIP1-XVAL DELX13=DELX1*DELX1*DELX1 XVAL-XI DELX1= RETURN SPLFUN=ABS(TEMP5) TEMP2=P2*DELX13/HI Y2=YIPl/HI P2=PIPl/6. Pl=PI/6. LOG(PORE RADIUS) LOG(PORE

RADIUS, PER UNIT AREA UNIT PER RADIUS, RADII BETWEEN THE LOWER AND THE UPPER THE AND LOWER THE BETWEEN RADII

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C REAL KRATE REAL Rl(50) REAL ETA(50),LCONV(50),LPRSTY(50) REAL CONC(50),LRATE(50) REAL OLDTAU(50),NEWTAU(50),OLDCNC(50),NEWCNC(50) COMMON/WORK/TAUFTR,CNVFTR,RTEFTR,RADFTR,EPLSN,FINFTR,FCORR COMMON/PARAM/KRATE,ALPHA,DB,DK,DS,VR,CZERO,CBULK COMMON/TABLE/TTABLE(100,50),RTABLE(100,50),PTABLE(100,50) COMMON/PELLET/RADIUS(50),RSQRD(50),DELRP,DELRSQ COMMON/COEFF/A1(50), A3 (50) DATA NEWCNC/50*0.0/ DATA OLDTAU,NEWTAU/100*0.0/ DATA OLDTM,NCALL/0.,0/ C C CONC=VECTOR CONTAINING THE LOCAL GAS CONCENTRATION CALCULATED C FROM A PSEUDO STEADY STATE MASS BALANCE C TIME=TIME SINCE THE BEGINNING OF REACTION C NPT=NUMBER OF GRID POINTS IN THE PELLET DIFFERENCE C REPRESENTATION OF THE PELLET C DELTM= TIME INCREMENT C LCONV=VECTOR CONTAINING THE VALUE OF THE LOCAL CONVERSION C LPRSTY=VECTOR CONTAINING THE VALUE OF LOCAL POROSITY C LRATE=VECTOR CONTAINING THE VALUE OF THE LOCAL RATE C LOCNPT=NPT NCALL=NCALL+1 IF(TIME.LE.OLDTM) GO TO 20 OLDTM=TIME IF(NCALL.GT.1) GO TO 5 DO 4 1=1,LOCNPT OLDCNC(I)=CONC(I) 4 CONTINUE GO TO 20 5 CONTINUE DO 10 1=1,LOCNPT OLDTAU(I)= NEWTAU(I) OLDCNC(I)= NEWCNC(I) 10 CONTINUE 20 CONTINUE DO 30 1=1,LOCNPT NEWCNC(I) = CONC(I) AVECNC =(NEWCNC(I)+OLDCNC(I))/2. NEWTAU(I)= OLDTAU(I) + AVECNC*DELTM/CZERO 30 CONTINUE DO 50 1=1,LOCNPT CALL NEWVAL(NEWTAU(I),A1(I),A3(I),LCONV(I),LPRSTY(I)) LRATE(I)=A3(I)*CONC(I)*RTEFTR C WRITE(6,*) I, 'RTABLE(1,I)= ',RTABLE(1,I) 50 CONTINUE RETURN END C SUBROUTINE NEWVAL(TAU,DIFF,RTE,CONV,PRSTY) C C THIS SUBROUTINE CALCULATES VALUES OF THE MACROSCOPIC C PROPERTIES OF THE POROUS MEDIUM FOR A GIVEN VALUE OF TAU. C IT INTERPOLATES OVER A CUBIC SPLINE USING SPLFUN. C COMMON/VALUES/TVALUE(100),DVALUE(100),RVALUE(100),PVALUE(100) COMMON/PVAL/DPVAL(100),RPVAL(100),PPVAL(100) COMMON/WORK/TAUFTR,CNVFTR,RTEFTR,RADFTR,EPSLN,FINFTR,FCORR

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 293

COMMON/LENGTH/NDIV C C TAU= INTEGRAL OF (C/CZERO) W.R.T TIME C DIFF= EFFECTIVE DIFFUSIVITY OF THE POROUS MEDIUM C RTE= EFFECTIVE REACTIVITY OF POROUS MEDIUM C CONV=CONVERSION OF THE SOLID REACTANT C PRSTY= POROSITY OF THE POROUS MEDIUM C LNDIV=NDIV TLOC=TAU DO 10 J=1,LNDIV IF(TLOC.LT.TVALUE(J)) GO TO 20 10 CONTINUE WRITE(6,100) TLOC STOP 20 CONTINUE I=J-1 DIFF = SPLFUN(TLOC,TVALUE(I) ,TVALUE(1+1),DVALUE(I) ,DVALUE(1+1), 1 DPVAL(I) , DPVAL(1 + 1)) RTE=SPLFUN(TLOC,TVALUE(I) ,TVALUE(1+1),RVALUE(I) , RVALUE(1+1), 1 RPVAL(I),RPVAL(1+1)) PRSTY=SPLFUN(TLOC,TVALUE(I),TVALUE(1 + 1),PVALUE(I),PVALUE(1+1) , 1 PPVAL(I),PPVAL(I+1)) CONV=(EPSLN-PRSTY)/CNVFTR IF(CONV.LE.1.E-12) CONV= 0. 100 FORMAT(///20X,'TAU IS OUT OF BOUNDS'/20X,'TAU =',E12.5) RETURN END C SUBROUTINE FINISH(CONV,LCONV,RATE,LRATE,PRSTY,LPRSTY, 1 RTEMAX,EFF,NPT) C C THIS SUBROUTINE INTEGRATES OVER THE ENTIRE PELLET TO C DETERMINE THE OVERALL VALUES OF THE MACROSCOPIC C PROPERTIES OF INTEREST C REAL LCONV(50),LRATE(50),LPRSTY(50) REAL RLRATE(50),RLCONV(50), RLPR(50) COMMON/COEFF/A1(50),A3(50) COMMON/PELLET/RADIUS(50),RSQRD(50),DELRP,DELRSQ COMMON/WORK/TAUFTR,CNVFTR,RTEFTR, RADFTR,EPSLN,FINFTR,FCORR C C CONV= OVERALL CONVERSION OF SOLID REACTANT C LCONV=VECTOR CONTAINING THE LOCAL CONVERSION C RATE= OVERALL RATE OF CHANGE OF CONVERSION C LRATE=VE CTOR CONTAINING THE VALUE OF THE LOCAL RATE C PRSTY=OVERALL POROSITY C LPRSTY=VECTOR CONTAINING LOCAL POROSITY C RTEMAX= RATE AT THE OUTSIDE THE PELLET WHEN T= 0. C EFF= EFFECTIVENESS FACTOR (RATE/RTFMAX) C NPT= NUMBER OF GRID POINTS IN THE FINITE DIFFERENCE C REPRESENTATION OF THE PELLET C LNPT=NPT DO 10 1=1,NPT RLRATE(I) = RSQRD(I)*LRATE(I) RLCONV(I)= RSQRD(I)*LCONV(I) RLPR(I) = RSQRD(I)*LPRSTY(I) 10 CONTINUE CALL SIMPSN(RLRATE,RTEMP,DELRP,LNPT) CALL SIMPSN(RLCONV,COTEMP,DELRP,LNPT) CALL SIMPSN(RLPR,PTEMP,DELRP,LNPT)

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RATE=RTEMP*RADFTR CONV=COTEMP *RADFTR PRSTY=PTEMP*RADFTR EFF=RATE/RTEMAX RETURN END C SUBROUTINE SIMPSN(F,FSUM,DELX,NPT) C C THIS SUBROUTINE EMPLOYS SIMPSON'S 2ND RULE OVER THE C FIRST FOUR POINTS AND THE COMPOSITE OF SIMPSON'S 1ST C RULE OVER THE REMAINING POINTS TO INTEGRATE THE FUNCTION C F. THIS SUBROUTINE REQUIRES THAT NPT BE AN EVEN VALUE. C REAL F(50),WT(6) DATA WT/9.,27.,27.,17.,4.,2./ C C F=VECTOR CONTAINING VALUES OF THE FUNCTION TO BE INTEGRATED C FSUM=INTEGRATED VALUE OF THE FUNCTION F. C DELX=THE STEP SIZE IN THE INDEPENDENT VARIABLE X C NPT=EVEN NUMBER, WHICH REPRESENTS THE NUMBER OF POINTS AT C WHICH F IS EVALUATED C LNPT=NPT FTOT=F(LNPT) DO 10 1=1,4 FTOT=FTOT+(WT(I)*F(I)/8.) 10 CONTINUE FTOT=FTOT+(WT (5)*F(5)) LIM=LNPT-2 DO 20 1=6,LIM,2 SUM=(WT(6)*F(I))+(WT(5)*F(I+1)) FTOT=FTOT+SUM 20 CONTINUE FSUM=FTOT*DELX/3. RETURN END C FUNCTION COMB(Rl) COMMON/PARAM/KRATE,ALPHA,DB,DK,DS,VR,CZERO,CBULK C C THIS FUNCTION CALCULATES THE DIFFUSIVITY THROUGH A SINGLE C PORE OF RADIUS Rl, TAKING INTO ACCOUNT THE COMBINATION OF C BULK AND KNUDSEN DIFFUSION C IF(R1.GT.0.) GO TO 10 COMB=0. RETURN 10 COMB=l./{(1./DB)+(1./DK/R1)) RETURN END C SUBROUTINE INTE(Rl,ETA,A1,A3,LPRSTY,NTOT) C C THIS SUBROUTINE EMPLOYS TWO POINT GAUSS-LEGENDRE C QUADRATURE TO INTEGRATE OVER ALL VALUES OF Rl AND C ETA TO OBTAIN MACROSCOPIC PROPERTIES OF THE POROUS C MEDIUM C EXTERNAL COMB REAL Rl(50),ETA(50),R1CUBE(50) REAL A1TEMP(50),A3TEMP(50)

0 CONTINUE 40 nonononnnn A3= EFFECTIVE REACTIVITY OF THE POROUS MEDIUM POROUS THE OF REACTIVITY MEDIUM POROUS EFFECTIVE THE A3= OF DIFFUSIVITY EFFECTIVE Al= NTOT=SIZE OF VECTORS Rl AND ETA AND Rl VECTORS OF MEDIUM NTOT=SIZE POROUS THE OF POROSITY LPRSTY=LOCAL RADII WITH PORES RADII OF INNER NUMBER THE THE OF VALUES CONTAINING THE ETA=VECTOR CONTAINING VECTOR Rl= A1=0. I=l,LOCN 10 DO LOCN=NTOT DO 30 J=I,LOCN 30 DO RETURN LPRSTY=0. A3=0. DATA Z/0.5773503/ DATA PI/3.14159/ DATA COMMON/PROP/RZERO(50),RZSQ(50,2) KRATE,LCFTR,LCONV,LPRSTY REAL R1TSQ(2) ,R1TEMP(2),F1TEMP(2),R2TSQ(2),R2TEMP(2),F3TEMP(2) REAL COMMON/TOTAL/ETASUM(50),EZERO(50),ETATOT COMMON/FACTOR/TRTSTY ,CZERO,CBULK ,V R S COMMON/PARAM/KRATE,ALPHA,DB,DK,D 1EPJ)=F1TEMP(1)+F1TEMP(2) A1TEMP(J K=1,2 25 DO R1TEMP(2)=(ZTEMP2+ZTEMP1)/2. R1TEMP(1)=(ZTEMP2-ZTEMP1)/2. A1LOC=0. )=F3TEMP(1)+F3TEMP(2) A3TEMP(J A3LOC=0. ) ZTEMP2=R1< J-1)+R1(J (J)-Rl(J-l)) ZTEMP1=Z*(Rl 20 TO GO IF(ETA(I).GT.0.) DO 40 J=I,LOCN 40 DO R1CUBE(1-1)=R1(1-1)*R1(1-1)*R1(1-1) Al=PI*AlLOC/TRTSTY/2. PLOC=0.0 PER UNIT AREA RADIUS, UNIT UNIT PER PER Rl AND Rl) (Rl-DELTA BETWEEN EP=1S() (ALPHA*RZSQ(J,K)) TEMP1=R1TSQ(K)- R1TSQ(K)=R1TEMP(K)*R1TEMP(K) EP=RTM( /S*LGRTM( )/R1TEMP(K)) TEMP3=(1./KRATE)+TEMP2 )/DS)*ALOG(R2TEMP(K TEMP2=(R2TEMP(K )) )=SQRT(R2TSQ(K R2TEMP(K )=TEMP1/(1.-ALPHA) R2TSQ(K )*COMB(R1TEMP(K)) )=R1TSQ(K F1TEMP(K A1L0C=A1L0C+{A1R1*DELR) ) )*ETA(J A3R1=A3TEMP(J )/TEMP3 )=R2TEMP(K F3TEMP(K A3L0C=A3L0C+(A3R1*DELR) )-Rl(J-l) DELR=R1(J )* ) A1TEMP(J ETA(J A1R1= 1UEJ)=R1(J)*Rl(J)*R1(J) R1CUBE(J PLOC=PLOC+PTEMP2 ) PTEMP2=PTEMP1*ETA(J )-RlCUBE(J-l) PTEMP1=R1CUBE(J

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A3=PI*A3LOC LPRSTY=PL0C*PI/3. RETURN END C SUBROUTINE SHOW(TIME,CONV,RATE,EFF,PRSTY,CONC,DEFF, 1 LCONV,LRATE,LPRSTY,NPTR,NITER) C C THIS SUBROUTINE PRINTS THE IMPORTANT VALUES CALCULATED C AT EACH TIME STEP C REAL DEFF(50),LCONV(50),LRATE(50),LPRSTY(50),CONC(50) C CHARACTER*20 LABEL(6) COMMON/PELLET/RADIUS(50),RSQRD(50),DELPR,DELRSQ COMMON/PARAM/KRATE,ALPHA,DB,DK,DS,VR,CZERO,CBULK COMMON/PRINT/IPRINT C DATA LABEL/ RADIUS, CONC, D(EFF), LCONV, C 1 LRATE, LPRSTY/ C C TIME= TIME SINCE THE REACTION BEGAN (SEC) C CONV= OVERALL CONVERSION IN THE PELLET C RATE= OVERALL RATE OF CHANGE OF CONVERSION (SEC-1) C EFF= EFFECTIVENESS FACTOR(RATE/RTEMAX) C PRSTY=OVERALL POROSITY (CM3/CM3) C CONC=VECTOR CONTAINING THE REACTANT GAS CONCENTRATION (MOLE/CM3) C DEFF= VECTOR CONTAINING THE EFFFECTIVE DIFFUSIVITY (CM2/SEC) C LCONV= VECTOR CONTAINING THE LOCAL CANVERSION C LRATE= VECTOR CONTAINING THE LOCAL REACTION RATE (SEC-1) C LPRSTY======POROSITY (CM3/CM3) C NPTR=NUMBER OF GRID POINTS IN THE FINITE DIFFERENCE AT THIS C TIME STEP C C IF (IPRINT.EQ.O) ONLY THE INTEGRATED VALUES ARE PRINTED OUT C IF (IPRINT.EQ.l) LOCAL VALUES ARE PRINTED OUT AT EVERY C (NPTR/10) GRID POINTS C IF (IPRINT.EQ.2) LOCAL VALUES ARE PRINTED OUT AT EVERY POINT C INC=NPTR/10 IF(IPRINT.EQ.2) INC=1 NPT=NPTR WRITE(6,510) TIME/60.,CONV,RATE,EFF,PRSTY IF(IPRINT.EQ.O) GO TO 10 WRITE(6,*) '(l)R(I) (2)C (I) (3)DE(I)(4)X(I) (5) KE(I)(6)E(I)' WRITE(6,520) (RADIUS(J)/RADIUS(NPT),J=INC,NPT,INC) WRITE(6,525) (CONC(J)/CBULK,J=INC,NPT,INC) WRITE(6,520) (DEFF(J),J=INC,NPT,INC) WRITE(6,520) (LCONV(J),J=INC,NPT,INC) WRITE(6,520) (LRATE(J),J=INC,NPT,INC) WRITE(6,520) (LPRSTY(J ),J=INC,NPT,INC) WRITE(6,530) NITER 10 CONTINUE NITER=0 510 FORMAT(5X,'TIME (MIN.)= ',E12.5,9X,'CONV= ',E12.5, 1 /9X,'RATE= ',E12.5,9X,'EFF= ',E12.5,/9X,'POROSITY= ',E12.5) 520 FORMAT(5X, 2(5E12.5/)) 525 FORMAT(5X, 2(5E12.5/)) 530 FORMAT(5X,'NUMBER OF ITERATIONS= ',13//) RETURN END C SUBROUTINE TRIDAG(IF,L,A,B,C,D,Y )

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C THIS SUBROUTINE SOLVES ANY SET OF LINEAR EQUATIONS C THAT CAN BE PUT INTO A TRIDIAGONAL MATRIX (FINITE C DIFFERENCE AND CUBIC SPLINE) C DIMENSION A(L),B(L),C(L),D(L),Y(L),BETA(301),GAMMA(301) C C IF = INDEX OF THE FIRST VALUE C L = INDEX OF THE LAST VALUE C A,B,C = VECTORS SPECIFYING THE COEFFICIENTS IN THE TRIDIAGONAL C MATRIX C D = VECTOR SPECIFYING THE CONSTANT TERM C Y = RESULTANT VECTOR FROM SOLVING THE (L-IF) LINEAR EQNS. C BETA(IF)= B (IF) GAMMA(IF)=D(IF)/BETA(IF) IFP1= IF+1 DO 1 I=IFP1,L BETA(I)=B(I)-A(I)*C(I-1)/BETA(1-1) 1 GAMMA(I)=(D(I)-A(I)*GAMMA(1-1))/BETA(I) Y (L)=GAMMA(L) LAST=L-IF DO 2 K=1,LAST I=L-K 2 Y(I)=GAMMA(I)-C(I)*Y(I+1)/BETA(I) RETURN END C SUBROUTINE DIFFEQ(CONC,CBULK,NPTR) C C THIS SUBROUTINE GENERATES A SET OF LINEAR EQUATIONS GENERATED C BY THE FINITE DIFFERENCE APPROXIMATION OF THE MASS BALANCE OF C A GAS DIFFUSING INTO A SPHERICAL PELLET WITH CHEMICAL REACTION. C C IT THEN SOLVES THESE EQUATIONS TO OBTAIN THE PSEUDO STEADY C STATE GAS CONCENTRATION PROFILE C REAL CONC(50) REAL A(50),B(50),C(50),D(50) COMMON/COEFF/DEFF(30),RK(50) COMMON/PELLET/RPEL(50),RPSQ(50),DELR,DELRSQ COMMON/WORK/TAUFTR,CNVFTR,RTEFTR,RADFTR,EPSLN,FINFTR,FCORR DATA A,B,C,D/49*0.0,1.0,150*0.0/ DATA IFIRST/1/ CC CC CONC=VECTOR CONTAINING THE CONCENTRATION OF THE REACTANT GAS CC CZERO= REACTANT GAS CONC. AT R=RZERO (OUTSIDE OR THE PELLET) CC NPTR = NUMBER OF GRID POINTS IN THE FINITE DIFFERENCE CC APPROXIMATION OF THE PELLET CC LNPT=NPTR-1 C (1)=-6.*DEFF(1)/DELRSQ B (1)=RK(l)-C(l) A (2)=-(RPSQ(2)*DEFF(2))/2. TEMP2=RPSQ(3)*DEFF(3) C (2)=(A (2)-TEMP2)/2. TEMP3=RPSQ(2)*RK(2)*DELRSQ B (2)=TEMP3-C(2)-A(2) DO 10 1=3,LNPT TEMP1=TEMP2 TEMP2=RPSQ(1+1)*DEFF(1+1) C (I)=-(TEMP1+TEMP2)/2. A (I )= C (1-1)

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TEMP3=RPSQ(I)*RK(I)*DELRSQ B (I)=TEMP3-C(I)-C(I-l) 10 CONTINUE LNPT= LNPT+1 FTR=FINFTR/DEFF(LNPT) A (LNPT)=FCORR B (LNPT)=(FTR/CBULK)-A(LNPT)+(DELRSQ*RK(LNPT)/DEFF(LNPT)/2.) D(LNPT)=FTR CALL TRIDAG(IFIRST,LNPT,A,B,C,D,CONC) RETURN END

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Data Input for Sorbent l

INPUT VALUE ______COMMENT______

2.5E-02 particle radius, cm 2.20 ratio of molar ratios of prod, and react. 0.15 bulk C02 mol fraction 1.0E-03 reaction rate constant, cm/s 1.0E-09 product layer diffusivity, cm2/s 3. tortuosity factor 1.0 molecular diffusivity, cm2/s 16.8 molar volume of solid reactant, cm3/mol 2.0 reaction time, hr 3.345 mass density of CaO, g/cm3 10. mass transfer coefficient, cm/s 650. reaction temperature, C 0.1 pore diameter base, /zm 0.05 maximum conversion increment 1. total pressure, atm 0.01 equilibrium C02 pressure, atm 1 2 20 0.1 .0 0.0907 .0006 0.0804 .0035 0.0724 .0115 0.0656 .0298 0.0604 .0504 0.0519 .1076 0.0402 .2106 0.0363 .2363 0.0303 .2607 0.0259 .268 0.0227 .2717 0.0202 .2737 0.0181 .275 0.013 .276 0.0101 .277 0.0091 .28 0.0065 .3 0.005 .34 0.004 .355

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Example of Output of Computer Program

MULTIPLE PORE MODEL

TEMPERATURE(DEG C)= 650.0

INPUT DATA

PELLET RADIUS(CM)= 0.25000E-01 RATIO OF MOLAR VOLUMES= 2.2000 BULK C02 CONCENTRATION(MOLES/CC)= 0.18481E-05 REACTION RATE CONCTANT(CM/SEC)= 0.10000E-02 PRODUCT LAYER DIFFUSIVITY(CM2/SEC)= 0.10000E-08 PELLET TURTUOSITY FACTOR= 3.00 BULK DIFFUSIVITY (CM2/SEC)= 0.10000E+01 KNUDSEN DIFFUSION COEFF. (CM/SEC)= 0.44431E+05 REACTANT MOLAR VOLUME= 16.8000 REACTION TIME(HRS)= 2.0000 VOLUME PER GRAM OF SOLID(CM3/GM)= 0.2990 MASS TRANSFER COEFF.= 10.00000 TOTAL NUMBER OF DATA POINTS= 20 MAXIMUM NUMBER OF DIVISION= 50 CONVERSION INCREMENT= 0.050

DIAMETER(CM)= CUMVOLUME(CM3/CM3)

0.10000E-04 0.0000 0.90700E-05 0.0009 0.80400E-05 0.0054 0.72400E-05 0.0176 0.65600E-05 0.0456 0.60400E-05 0.0771 0.51900E-05 0.1645 0.40200E-05 0.3220 0.36300E-05 0.3613 0.30300E-05 0.3987 0.25900E-05 0.4098 0.22700E-05 0.4155 0.20200E-05 0.4185 0.18100E-05 0.4205 0.13000E-05 0.4220 0.10100E-05 0.4236 0.91000E-06 0.4282 0.65000E-06 0.4587 0.50000E-06 0.5199 0.40000E-06 0.5429 RZERO ETASUM EZERO

0.20000E-06 0.00000E+00 0.00000E+00 0.22500E-06 0.85246E+11 0.34098E+19 0.25000E-06 0.61061E+11 0.24424E+19 0.28750E-06 0.14337E+12 0.38231E+19 0.32500E-06 0.96886E+11 0.25836E+19 0.39000E-06 0.41160E+11 0.63323E+18 0.45500E-06 0.24936E+11 0.38362E+18 0.48000E-06 0.34268E+10 0.13707E+18 0.50500E-06 0.29310E+10 0.11724E+18 0.57750E-06 0.88173E+09 0.12162E+17 0.65000E-06 0.60472E+09 0.83409E+16

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0.77750E-06 0.51572E+09 0.40449E+16 0.90500E-06 0.31498E+09 0.24704E+16 0.95750E-06 0.37473E+09 0.71377E+16 0.10100E-05 0.31787E+09 0.60548E+16 0.10725E-05 0.46187E+09 0.73900E+16 0.11350E-05 0.38778E+09 0.62045E+16 0.12150E-05 0.67346E+09 0.84183E+16 0.12950E-05 0.55271E+09 0.69089E+16 0.14050E-05 0.10125E+10 0.92042E+16 0.15150E-05 0.80043E+09 0.72766E+16 0.16650E-05 0.24530E+10 0.16354E+17 0.18150E-05 0.18718E+10 0.12478E+17 0.19125E-05 0.18461E+10 0.18935E+17 0.20100E-05 0.15843E+10 0.16249E+17 0.23025E-05 0.57261E+10 0.19576E+17 0.25950E-05 0.39095E+10 0.13366E+17 0.28075E-05 0.19791E+10 0.93132E+16 0.30200E-05 0.15769E+10 0.74206E+16 0.31500E-05 0.53757E+09 0.41352E+16 0.32800E-05 0.47496E+09 0.36535E+16 0.34500E-05 0.40293E+09 0.23702E+16 0.36200E-05 0.34755E+09 0.20444E+16 0.38200E-05 0.14434E+09 0.72171E+15 0.40200E-05 0.12336E+09 0.61679E+15 0.42775E-05 0.42226E+08 0.16399E+15 0.45350E-05 0.35247E+08 0.13688E+15 0.47675E-05 0.69128E+07 0.29732E+14 0.50000E-05 0.59717E+07 0.25685E+14 TAU DIFFUSIVITY RATE CONST. POROS]

0.00000E+00 0.14342E-01 0.11871E+04 0.54285E+00 0.36218E-01 0.14328E-01 0.11873E+04 0.54205E+00 0.81661E-01 0.14310E-01 0.11877E+04 0.54104E+00 0.12275E+00 0.14293E-01 0.11879E+04 0.54014E+00 0.18226E+00 0.14269E-01 0.11883E+04 0.53882E+00 0.22831E+00 0.14251E-01 0.11885E+04 0.53781E+00 0.31585E+00 0.14216E-01 0.11890E+04 0.53588E+00 0.36931E+00 0.14195E-01 0.11893E+04 0.53470E+00 0.47842E+00 0.14I51E-01 0.11897E+04 0.53231E+00 0.53948E+00 0.14127E-01 0.11899E+04 0.53097E+00 0.72171E+00 0.14056E-01 0.11904E+04 0.52698E+00 0.79583E+00 0.14026E-01 0.11906E+04 0.52536E+00 0.10166E+01 0.13941E-01 0.11908E+04 0.52055E+00 0.11042E+01 0.13907E-01 0.11908E+04 0.5I865E+00 0.12585E+01 0.13847E-01 0.11906E+04 0.51531E+00 0.13520E+01 0.13811E-01 0.11904E+04 0.51329E+00 0.15222E+01 0.13746E-01 0.11900E+04 0.50961E+00 0.16218E+01 0.13709E-0I 0.11896E+04 0.50746E+00 0.19733E+01 0.13576E-01 0.11878E+04 0.49992E+00 0.20890E+01 0.13533E-01 0.11870E+04 0.49745E+00 0.24880E+01 0.13386E-01 0.11836E+04 0.48896E+00 0.26204E+01 0.13338E-01 0.11822E+04 0.48615E+00 0.33086E+01 0.13091E-01 0.11729E+04 0.47168E+00 0.34705E+01 0.13034E-01 0.11701E+04 0.46830E+00 0.42500E+01 0.12765E-01 0.11534E+04 0.45217E+00 0.44430E+01 0.12700E-01 0.11483E+04 0.44821E+00 0.49171E+01 0.12542E-01 0.11334E+04 0.43855E+00 0.51253E+01 0.12474E-01 0.11257E+04 0.43433E+00 0.56407E+01 0.12308E-01 0.10978E+04 0.42385E+00 0.58649E+01 0.12238E-01 0.10659E+04 0.41947E+00 0.64871E+01 0.12047E-01 0.95516E+03 0.40791E+00 0.67305E+01 0.11974E-01 0.92055E+03 0.40375E+00

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0.74059E+01 0.11777E-01 0.80277E+03 0.39248E+00 0.76695E+01 0.11703E-01 0.75095E+03 0.38875E+00 0.85314E+01 0.11466E-01 0.58398E+03 0.37757E+00 0.88212E+01 0.11389E-01 0.54486E+03 0.37451E+00 0.97580E+01 0.11146E-01 0.43168E+03 0.36547E+00 0.10075E+02 0.11066E-01 0.41792E+03 0.36286E+00 0.11354E+02 0.10751E-01 0.36369E+03 0.35288E+00 0.11709E+02 0.10665E-01 0.34808E+03 0.35021E+00 0.13104E+02 0.10338E-01 0.30911E+03 0.34099E+00 0.13500E+02 0.10247E-01 0.29886E+03 0.33849E+00 0.15429E+02 0.98160E-02 0.26928E+03 0.32717E+00 0.15883E+02 0.97171E-02 0.26508E+03 0.32462E+00 0.17997E+02 0.92687E-02 0.25349E+03 0.31301E+00 0.18513E+02 0.91620E-02 0.25077E+03 0.31022E+00 0.20197E+02 0.88217E-02 0.24260E+03 0.30129E+00 0.20762E+02 0.87100E-02 0.23993E+03 0.29833E+00 0.22582E+02 0.83584E-02 0.23201E+03 0.28897E+00 0.23199E+02 0.82419E-02 0.22944E+03 0.28584E+00 0.27897E+02 0.73996E-02 0.21134E+03 0.26279E+00 0.28653E+02 0.72711E-02 0.20866E+03 0.25920E+00 0.33907E+02 0.64277E-02 0.19053E+03 0.23511E+00 0.34819E+02 0.62898E-02 0.18754E+03 0.23109E+00 0.39317E+02 0.56444E-02 0.17347E+03 0.21190E+00 0.40364E+02 0.55020E-02 0.17039E+03 0.20759E+00 0.45322E+02 0.48671E-02 0.15640E+03 0.18794E+00 0.46522E+02 0.47226E-02 0.15323E+03 0.18337E+00 0.50324E+02 0.42873E-02 0.14354E+03 0.16936E+00 0.51642E+02 0.41440E-02 0.14027E+03 0.16466E+00 0.55769E+02 0.37204E-02 0.13047E+03 0.15049E+00 0.57219E+02 0.35797E-02 0.12721E+03 0.14566E+00 0.62631E+02 0.30937E-02 0.11491E+03 0.12860E+00 0.64254E+02 0.29589E-02 0.11117E+03 0.12378E+00 0.70173E+02 0.25082E-02 0.98366E+02 0.10728E+00 0.71990E+02 0.23818E-02 0.94947E+02 0.10255E+00 0.79290E+02 0.19264E-02 0.81286E+02 0.84865E-01 0.81347E+02 0.18121E-02 0.77373E+02 0.80293E-01 0.89374E+02 0.14171E-02 0.62957E+02 0.63728E-01 0.91702E+02 0.13211E-02 0.59397E+02 0.59780E-01 0.10242E+03 0.94704E-03 0.44402E+02 0.43970E-01 0.10511E+03 0.86834E-03 0.40834E+02 0.40456E-01 0.11701E+03 0.59556E-03 0.29434E+02 0.28578E-01 0.12012E+03 0.53696E-03 0.26901E+02 0.25915E-01 0.13234E+03 0.35720E-03 0.18574E+02 0.17629E-01 0.13591E+03 0.31563E-03 0.16727E+02 0.15656E-01 0.14945E+03 0.19835E-03 0.10869E+02 0.10010E-01 0.15354E+03 0.17205E-03 0.94940E+01 0.87258E-02 0.15776E+03 0.14848E-03 0.81694E+01 0.75703E-02 0.16212E+03 0.12730E-03 0.69524E+01 0.65374E-02 0.16663E+03 0.10825E-03 0.60576E+01 0.55985E-02 0.17130E+03 0.91468E-04 0.52119E+01 0.47573E-02 0.17614E+03 0.76711E-04 0.44489E+01 0.40136E-02 0.18118E+03 0.63689E-04 0.37343E+01 0.33510E-02 0.18642E+03 0.52411E-04 0.31315E+01 0.27711E-02 0.19189E+03 0.42646E-04 0.26095E+01 0.22580E-02 0.19761E+03 0.34425E-04 0.21091E+01 0.18191E-02 0.20361E+03 0.27655E-04 0.16796E+01 0.14609E-02 0.20992E+03 0.21933E-04 0.12848E+01 0.11657E-02 0.21659E+03 0.17112E-04 0.99360E+00 0.92207E-03 0.22368E+03 0.13057E-04 0.80270E+00 0.71122E-03 0.23123E+03 0.97184E--05 0.61720E+00 0.53257E-03 0.23936E+03 0.71497E-05 0.45882E+00 0.39425E-03 0.24817E+03 0.51039E-05 0.31460E+00 0.28831E-03

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 303

0.25785E+03 0.34138E-05 0.22750E+00 0.20310E-03 0.26865E+03 0.20966E-05 0.16752E+00 0.13115E-03 0.28102E+03 0.11423E-05 0.10995E+00 0.74821E-04 0.29579E+03 0.52967E-06 0.58266E-01 0.36338E-04 0.31510E+03 0.15137E-06 0.24237E-01 0.13041E-04 0.35789E+03 0.OOOOOE+OO 0.00000E+00 0.OOOOOE+OO RTEMAX= 0.803441405E-01 TAU DIFFUSIVITY RATE CONST. POROSITY

0.OOOOOE+OO 0.14342E-01 0.11871E+04 0.54285E+00 0.48878E-01 0.14328E-01 0.11873E+04 0.54205E+00 0.11020E+00 0.14310E-01 0.11877E+04 0.54104E+00 0.16565E+00 0.14293E-01 0.11879E+04 0.54014E+00 0.24596E+00 0.14269E-01 0.11883E+04 0.53882E+00 0.30811E+00 0.14251E-01 0.11885E+04 0.53781E+00 0.42625E+00 0.14216E-01 0.11890E+04 0.53588E+00 0.49840E+00 0.14195E-01 0.11893E+04 0.53470E+00 0.64564E+00 0.14151E-01 0.11897E+04 0.53231E+00 0.72804E+00 0.14127E-01 0.11899E+04 0.53097E+00 0.97398E+00 0.14056E-01 0.11904E+04 0.52698E+00 0.10740E+01 0.14026E-01 0.11906E+04 0.52536E+00 0.13720E+01 0.13941E-01 0.11908E+04 0.52055E+00 0.14902E+01 0.13907E-01 0.11908E+04 0.51865E+00 0.16983E+01 0.13847E-01 0.11906E+04 0. 51531E+00 0.18245E+01 0.13811E-01 0.11904E+04 0.51329E+00 0.20543E+01 0.13746E-01 0.11900E+04 0.50961E+00 0.21887E+01 0.13709E-01 0.11896E+04 0.50746E+00 0.26630E+01 0.13576E-01 0.11878E+04 0.49992E+00 0.28191E+01 0.13533E-01 0.11870E+04 0.49745E+00 0.33576E+01 0.13386E-01 0.11836E+04 0.48896E+00 0.35364E+01 0.13338E-01 0.11822E+04 0.48615E+00 0.44650E+01 0.13091E-01 0.11729E+04 0.47168E+00 0.46836E+01 0.13034E-01 0.11701E+04 0.46830E+00 0.57354E+01 0.12765E-01 0.11534E+04 0.45217E+00 0.59959E+01 0.12700E-01 0.11483E+04 0.44821E+00 0.66357E+01 0.12542E-01 0.11334E+04 0.43855E+00 0.69167E+01 0.12474E-01 0.11257E+04 0.43433E+00 0.76124E+01 0.12308E-01 0.10978E+04 0.42385E+00 0.79149E+01 0.12238E-01 0.10659E+04 0.41947E+00 0.87545E+01 0.12047E-01 0.95516E+03 0.40791E+00 0.90829E+01 0.11974E-01 0.92055E+03 0.40375E+00 0.99944E+01 0.11777E-01 0.80277E+03 0.39248E+00 0.10350E+02 0.11703E-01 0.75095E+03 0.38875E+00 0.11513E+02 0.11466E-01 0.58397E+03 0.37757E+00 0.11904E+02 0.11389E-01 0.54486E+03 0.37451E+00 0.13169E+02 0.11146E-01 0.43168E+03 0.36546E+00 0.13597E+02 0.11066E-01 0.41792E+03 0.36286E+00 0.15322E+02 0.10751E-01 0.36369E+03 0.35288E+00 0.15802E+02 0.10665E-01 0.34808E+03 0.35021E+00 0.17684E+02 0.10338E-01 0.30911E+03 0.34099E+00 0.18219E+02 0.10247E-01 0.29886E+03 0.33849E+00 0.20821E+02 0.98160E-02 0.26928E+03 0.32717E+00 0.21434E+02 0.97171E-02 0.26508E+03 0.32462E+00 0.24287E+02 0.92687E-02 0.25349E+03 0.31301E+00 0.24984E+02 0.91620E-02 0.25077E+03 0.31022E+00 0.27256E+02 0.88217E-02 0.24260E+03 0.30129E+00 0.28018E+02 0.87100E-02 0.23993E+03 0.29833E+00 0.30475E+02 0.83584E-02 0.23201E+03 0.28897E+00 0.31308E+02 0.82419E-02 0.22944E+03 0.28584E+00 0.37648E+02 0.73996E-02 0.21134E+03 0.26279E+00 0.38668E+02 0.72711E-02 0.20866E+03 0.25920E+00 0.45758E+02 0.64277E-02 0.19053E+03 0.23511E+00

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 304

0.46989E+02 0.62898E-02 0.18754E+03 0.23109E+00 0.53059E+02 0.56444E-02 0.17347E+03 0.21190E+00 0.54473E+02 0.55020E-02 0.17039E+03 0.20759E+00 0.61164E+02 0.48671E-02 0.15640E+03 0.18794E+00 0.62782E+02 0.47226E-02 0.15323E+03 0.18337E+00 0.67913E+02 0.42873E-02 0.14354E+03 0.16936E+00 0.69693E+02 0.41440E-02 0.14027E+03 0.16466E+00 0.75261E+02 0.37204E-02 0.13047E+03 0.15049E+00 0.77219E+02 0.35797E-02 0.12721E+03 0.14566E+00 0.84522E+02 0.30937E-02 0.11491E+03 0.12860E+00 0.86713E+02 0.29589E-02 0.11117E+03 0.12378E+00 0.94701E+02 0.25082E-02 0.98366E+02 0.10728E+00 0.97152E+02 0.23818E-02 0.94947E+02 0.10255E+00 0.10700E+03 0.19264E-02 0.81286E+02 0.84865E-01 0.10978E+03 0.18121E-02 0.77373E+02 0.80293E-01 0.12061E+03 0.14171E-02 0.62957E+02 0. 63728E-01 0.12376E+03 0.13211E-02 0.59397E+02 0.59780E-01 0.13821E+03 0.94704E-03 0.44402E+02 0.43970E-01 0.14185E+03 0.86834E-03 0.40834E+02 0.40456E-01 0.15790E+03 0.59556E-03 0.29434E+02 0.28578E-01 0.16210E+03 0.53696E-03 0.26901E+02 0.25915E-01 0.17860E+03 0.35720E-03 0.18574E+02 0.17629E-01 0.18341E+03 0.31563E-03 0.16727E+02 0.15656E-01 0.20169E+03 0.19835E-03 0.10869E+02 0.10010E-01 0.20721E+03 0.17205E-03 0.94940E+01 0.87258E-02 0.21290E+03 0.14848E-03 0.81694E+01 0.75702E-02 0.21878E+03 0.12730E-03 0.69524E+01 0.65374E-02 0.22487E+03 0.10825E-03 0.60576E+01 0.55985E-02 0.23117E+03 0.91468E-04 0.52119E+01 0.47574E-02 0.23771E+03 0.76711E-04 0.44489E+01 0.40136E-02 0.24450E+03 0.63689E-04 0.37343E+01 0.33510E-02 0.25158E+03 0.52410E-04 0.31315E+01 0.27711E-02 0.25896Et 03 0.42646E-04 0.26095E+01 0.22580E-02 0.26668E+03 0.34425E-04 0.21091E+01 0.18191E-02 0.27478E+03 0.27655E-04 0.16796E+01 0.14609E-02 0.28330E+03 0.21933E-04 0.12848E+01 0.11657E-02 0.29230E+03 0.17112E-04 0.99361E+00 0.92207E-03 0.30186E+03 0.13058E-04 0.80270E+00 0.71122E-03 0.31206E+03 0.97185E-05 0.61720E+00 0.53257E-03 0.32302E+03 0.71497E-05 0.45882E+00 0.39425E-03 0.33491E+03 0.51039E-05 0.31460E+00 0.28831E-03 0.34797E+03 0.34139E-05 0.22750E+00 0.20310E-03 0.36255E+03 0.20966E-05 0.16752E+00 0.13115E-03 0.37924E+03 0.11423E-05 0.10995E+00 0.74821E-04 0.39918E+03 0.52967E-06 0.58266E-01 0.36338E-04 0.42523E+03 0.15137E-06 0.24237E-01 0.13041E-04 0.48298E+03 0.00000E+00 0.OOOOOE+OO 0.OOOOOE+OO RTEMAX= 0.595348999E-01 1 TPLUG= 0.48250E+03 RXNSEC= 0.72000E+04 AREA(CM2/G 0.77902E+06 TIME (MIN.)= 0.00000E+00 CONV= 0.96701E-05 RATE= 0. 21398E-01 EFF= 0.35943E+00 POROSITY= 0.54285E+00 (1)RI (2)CI (3)DE (4)X(I) (5) KE (6)EI 0.81633E-01 0.18367E+00 0.28571E+00 0.38776E+00 0.48980E+00 0.59184E+00 0.69388E+00 0.79592E+00 0.89796E+00 0.10000E+01

0.85758E-02 0.10645E-01 0.15073E-01 0.23407E-01 0.38678E-01 0.66668E-01 0.11838E+00 0.21484E+00 0.39641E+00 0.74100E+00

0.14342E-01 0.14342E-01 0.14342E-01 0.14342E-01 0.14342E-01 0.14342E-01 0.14342E-01 0.14342E-01 0.14342E-01 0.14342E-01

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 305

0.96701E-05 0.96701E-05 0.96701E-05 0.96701E-05 0.96701E-05 0.96701E-05 0.96701E-05 0.96701E-05 0.96701E-05 0.96701E-05

0.68901E-03 0.85523E-03 0.12110E-02 0.18806E-02 0.31075E-02 0.53564E-02 0.95114E-02 0.17261E-01 0.31849E-01 0.59535E-01

0.54285E+00 0.54285E+00 0.54285E+00 0.54285E+00 0.54285E+00 0.54285E+00 0.54285E+00 0.54285E+00 0.54285E+00 0.54285E+00

NUMBER OF ITERATIONS= 1

TIME (MIN.)= 0.38944E-01 CONV= 0.24887E-01 RATE= 0.21452E-01 EFF= 0.36032E+00 POROSITY= 0.52920E+00 (1)RI (2)Cl (3)DE (4)X(I) (5) KE (6)El 0.81633E-01 0.18367E+00 0.28571E+00 0.38776E+00 0.48980E+00 0.59184E+00 0.69388E+00 0.79592E+00 0.89796E+00 0.10000E+01

0.85758E-02 0.10645E-01 0.15073E-01 0.23407E-01 0.38678E-01 0.66668E-01 0.11838E+00 0.21484E+00 0.39641E+00 0.74100E+00

0.14334E-01 0.14332E-01 0.14328E-01 0.14320E-01 0.14306E-01 0.14280E-01 0.14232E-01 0.14142E-0I 0.13976E-01 0.13667E-01

0.81772E-03 0.10125E-02 0.14294E-02 0.22137E-02 0.36497E-02 0.62811E-02 0.11135E-01 0.20163E-01 0.37063E-01 0.68805E-01

0.68910E-03 0.85536E-03 0.12113E-02 0.18812E-02 0.31091E-02 0.53610E-02 0.95250E-02 0.17301E-01 0.31947E-01 0.59637E-01

0.54240E+00 0.54230E+00 0.54207E+00 0.54164E+00 0.54085E+00 0.53941E+00 0.53674E+00 0.53179E+00 0.52252E+00 0.50511E+00

NUMBER OF ITERATIONS= 1

TIME (MIN.)= 0.77791E-01 CONV= 0.48828E-01 RATE= 0.20936E-01 EFF= 0.35166E+00 POROSITY= 0.51606E+00 (1)RI (2)CI (3)DE (4)X(I) (5) KE (6)EI 0.81633E-01 0.18367E+00 0.28571E+00 0.38776E+00 0.48980E+00 0.59184E+00 0.69388E+00 0.79592E+00 0.89796E+00 0.10000E+01

0.80557E-02 0.10002E-01 0.14171E-01 0.22029E-01 0.36464E-01 0.63044E-01 0.11256E+00 0.20628E+00 0.38747E+00 0.74784E+00

0.14327E-01 0.14323E-01 0.14315E-01 0.14299E-01 0.14271E-01 0.14220E-01 0.14126E-01 0.13951E-01 0.13630E-01 0.13041E-01

0.15916E-02 0.19729E-02 0.27891E-02 0.43249E-02 0.71402E-02 0.12296E-01 0.21812E-01 0.39523E-01 0.72719E-01 0.13515E+00

0.64737E-03 0.80383E-03 0.11390E-02 0.17709E-02 0.29325E-02 0.50731E-02 0.90650E-02 0.16625E-01 0.31171E-01 0.59241E-01

0.54198E+00 0.54177E+00 0.54132E+00 0.54048E+00 0.53894E+00 0.53611E+00 0.53089E+00 0.52117E+00 0.50296E+00 0.46871E+00

NUMBER OF ITERATIONS= 3

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 306

TIME (MIN.)= 0.11759E+00 CONV= 0.72476E-01 RATE= 0.20563E-01 EFF= 0.34540E+00 POROSITY= 0.50309E+00 (1)RI (2)CI (3)DE (4)X(I) (5) KE (6)EI 0.81633E-01 0.18367E+00 0.28571E+00 0.38776E+00 0.48980E+00 0.59184E+00 0.69388E+00 0.79592E+00 0.89796E+00 0.10000E+01

0.78618E-02 0.97627E-02 0.13836E-01 0.21518E-01 0.35648E-01 0.61722E-01 0.11048E+00 0.20339E+00 0.38511E+00 0.75301E+00

0.14319E-01 0.14314E-01 0.14302E-01 0.14279E-01 0.14237E-01 0.14162E-01 0.14023E-01 0.13766E-01 0.13295E-01 0.12445E-01

0.23447E-02 0.29079E-02 0.41134E-02 0.63836E-02 0.10543E-01 0.18170E-01 0.32260E-01 0.58533E-01 0.10793E+00 0.20114E+00

0.63187E-03 0.78471E-03 0.11123E-02 0.17304E-02 0.28680E-02 0.49695E-02 0.89022E-02 0.16383E-01 0.30778E-01 0.57221E-01

0.54157E+00 0.54126E+00 0.54060E+00 0.53935E+00 0.53707E+00 0.53288E+00 0.52515E+00 0.51074E+00 0.48364E+00 0.43251E+00

NUMBER OF ITERATIONS= 3

TIME (MIN.)= 0.15812E+00 CONV= 0.95698E-01 RATE= 0.19770E-01 EFF= 0.33207E+00 POROSITY= 0.49035E+00 (1)RI (2)CI (3)DE (4)X(I) (5) KE (6)EI 0.81633E-01 0.18367E+00 0.28571E+00 0.38776E+00 0.48980E+00 0.59184E+00 0.69388E+00 0.79592E+00 0.89796E+00 0.10000E+01

0.77664E-02 0.96455E-02 0.13674E-01 0.21275E-01 0.35275E-01 0.61161E-01 0.10974E+00 0.20293E+00 0.38711E+00 0.76359E+00

0.14312E-01 0.14304E-01 0.14288E-01 0.14259E-01 0.14204E-01 0.14104E-01 0.13322E-01 0.13585E-01 0.12971E-01 0.11893E-01

0.30868E-02 0.38293E-02 0.54193E-02 0.84128E-02 0.13900E-01 0.23963E-01 0.42569E-01 0.77312E-01 0.14272E+00 0.26216E+00

0.62426E-03 0.77538E-03 0.10994E-02 0.17113E-02 0.28390E-02 0.49264E-02 0.88446E-02 0.16316E-01 0.30569E-01 0.45325E-01

0.54116E+00 0.54075E+00 0.53988E+00 0.53824E+00 0.53523E+00 0.52971E+00 0.51950E+00 0.50044E+00 0.46456E+00 0.39904E+00

NUMBER OF ITERATIONS= 3

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Vita

Arpaden Silaban, son of Mula Silaban and Nona B.

Hutasoit, was born on November 12, 1955 in Tarutung, North

Sumatra, Indonesia. He completed his Engineer's degree in

Chemical Engineering at University of Sriwijaya, Palembang,

Indonesia in January 1980. He joined that university

following the graduation. In 1986, he was awarded from

Indonesian government a scholarship on Master's degree

program at Louisiana State University. He finished his Master

of Science in Chemical Engineering in Spring 1989. Beginning

Summer 1989 he started to pursue his doctoral degree. He is

presently completing the requirements for the Doctor of

Philosophy degree.

He married Doorce Sakti Batubara, daughter of M.

Batubara and R. Simangunsong, on October 12, 1985. They both

are blessed with a son, Athens Gomes Partogi Silaban, now 6

years old. God willing, they are now expecting the second

child to be named Grace Rouge Pastima Silaban.

307

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DOCTORAL EXAMINATION AND DISSERTATION REPORT

candidate: Arpaden Silaban

Major Field: Chemical Engineering

Title of Dissertation: High-Temperature High-Pressure C0? Removal from Coal Gas

Approved: / , /. l,--) ( „ Major Professor and Chairman

Dehn of the Gradii§£e School

EXAMINING COMMITTEE:

Date of Examination:

April 6, 1993

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.